As per Adwaitha - Siddhantha, after a person's death, Aatma will merge with supreme one, called Paramathma.
My question is, how can we know that an Aatma got Moksha? Is there any way to identify it?
No there isn't any way to identify that one got mokshya or not as no one has any idea about how the atma is(as its so small as mentioned below and no ordinary human being can see it without the help of supreme Lord) and whose atma it is, only paramathma knows about it.
When the upper point of a hair is divided into one hundred parts and again each of such parts is further divided into one hundred parts, each such part is the measurement of the dimension of the spirit soul.
Source : Śvetāśvatara Upaniṣad (5.9)
As per Advaita, Aatma donot exist, only Brahman(consciousness) exists, Aatma is just a temporary reflection of consciousness, existing in heart. This soul needs to be destroyed to attain Kaivalya Moksha. This is explained by Jad Bharat in Vishnu Puran
Meditation on self, again, is said to be for the sake of supreme truth; but the object of this is to establish distinctions (between soul and body), and the great truth of all is without distinctions. Union of self with supreme spirit is said to be the great end of all; but this is false; for one substance cannot become substantially another. What the great end of all is, you shall, monarch, briefly learn from me. It is Brahman: one (in all bodies), pervading, uniform, perfect, preeminent over nature (Prakriti), exempt from birth, growth, and decay, omnipresent, undecaying, made up of true knowledge, independent, and unconnected with unrealities, with name, species, and the rest, in time present, past, or to come.
This is also explained in Shiva Geeta, that destruction of soul, is required to attain Kaivalya Moksha(non-dual union with Brahman).
The piercing of Sahasrara is done by Yogis, to go to higher realms(within 14 realms of Brahma), when their soul escapes the body, as they have control over their soul and prana, while for normal people, soul escapes through Prana that is controlled by Ishwar/Prakriti(reference Raman Mahrshi's work "Who am I"). But for gyanis, neither soul exists nor Prakriti exists, only Purush/Brahman made of pure consciousness exists. Their liberation is explained in Avadhut Geeta by Dattatreya as a union of pot space into universal Space.
On the destruction of a jar, the space in it unites with all space. In myself and Shiva I see no difference when the mind is purified.
In whatever place and in whatever state gyani dies, his spirit is absorbed into That, as, on the destruction of the jar, the space in the jar is united with absolute space.
Whether he dies conscious or in coma, in a holy temple or in the house of an untouchable, he obtains liberation, becoming the all-pervading Brahman.
There is only one physical trace of knowing that the atman is ejected by passing from Sahastradal Kamal(The Thousand Petal Lotus) Known as Opening the crown of head.
The Atman for a general being is released or ejected form nostrils.In examining body of Swami Vivekananda doctors reported Rupture of blood vessels in brain. See this for death report of Swami Vivekananda.
There are more ways but are out of scope considering the situation nowadays.(Yogic Method's and Surpassing your self upto the Bramha Loka).
The primary object of Moksha is knowledge itself. Nearly all schools of thought that acknowledge jivanmukta, acknowledge Ignorance (avidya) as the sole source of all evil and suffering. Buddhism, Jainism, Samkhya, and Vedanta are all agreed on this. There is even an extreme sect of the Shīʿa Muslims known as the the Nuṣayrī-ʿAlawīs who believe in liberation from birth and death in a similar manner. The same probably goes for the Sikhs. Even the Bhagavad Gita places a great emphasis on knowledge, claiming that an extremely sinful person could cross over the entirety of Samsara, with the aid of knowledge alone.
A soul "knows" that it has attained Moksha because knowledge is a soul's innate nature. Knowledge is also always correct (or else it wouldn't be knowledge). Since knowledge is "comprehensive" (it knows all there is to know) it illuminates both itself and the object of knowledge.
In other words a person possesses knowledge because the object of knowledge is something real, something true (Brahman). Cognizance of something real and true corrects one's perception and destroys ignorance (it makes the knowledge valid). Thereafter, the questions about knowledge, "how," and so on and so forth, all dissolve as non-questions.
That's the best way I can put it.
Passions attract the flow of karmic matter into the souls. And passions are due to ignorance. So ignorance is the real cause of bondage. Here Jainism agrees with Sankhya, Buddhism and Vedanta. Now, ignorance can be removed only by knowledge. So right knowledge is the cause of liberation. (A Critical Survey of Indian Philosophy, by Chandradhar Sharma, page 65.)
Al-Tabarani opens his work with the recurrent Nusayri injunction to attain the gnostic mystery of the divinity. Moreover, according to a tradition ascribed to the Imam al-Hasan al-Askari—on whose authority many traditions in Kitab al-ma'arif are transmitted—God in fact exempted His creatures from worshiping Him through religious commandments and only "wanted them to know Him, for gnosis is the worship of God" (fa-ma arada minhum illa al-ma'rifa wa-hiya al-ibada). (Dogma and Ritual in Kitab al-Ma'arif, by M.M. Bar-Asher and Aryeh Kofsky, page 49.)
Gnosis means to "know," or "knowledge."
Basically, knowledge (or gnosis), is the indisputable bottom line of liberation, in any religious or spiritual tradition (whether Hindu, Buddhist, Muslim, theistic, or atheistic, or whatever). Even non-religious teachers emphasize a form of epistemic knowledge that arises after enlightenment (cf. Stephen Jourdain, Jed McKenna, and Philip Goddard).
If one thinks about "Me" (i.e. nothingness) while death, then one attains Moksha/"Me" [BG 4.32, 5.28]. How do we know that person is thinking about "Me" -- depends on at what time one leaves the physical body.
Bhagavad Gita describes physical signs of Moksha; If a person dies when,
Except the 4th one (if doubtful), all the other attributes are physically verifiable. If there is a Night of anyone of Deva, Pitru or humans, then the Moksha is not attained.
BG 8.23 - The time, having departed at, which practitioners (yogi-s), attain the State of No-return, and also [of the time which attains] the state of return, shall be described by me, O best of Bharata-s.
BG 8.24 - [In presence of] Agni [AND] bright daytime [AND] the bright fortnight (Shukla-paksha) [AND] the six months of the Northern solstice (UttarAyana) -- by following this Path, persons who are knowers of Brahman attain Brahman when they die.
BG 8.25 - Smoke [OR] nigh [OR] as also the dark fortnight [OR] the six months of the Southern solstice-following this Path the yogi having reached the lunar light, returns.
BG 8.26 - These two courses of the world, which are white and black, are verily considered eternal. By the one a man goes to the State of Non-return; by the other he returns again.
Since Moksha is rare, I have paid attention to the placing of [AND] & [OR].
So does it mean that "Moksha lovers", once knowing this knowledge, should strive for deciding the death-day all the time?
Answer is No, ;-) Krishna further says:
BG 8.27 - O son of Prtha, no yogi whosoever has known these two courses becomes deluded. Therefore, O Arjuna, be you steadfast in yoga at all times.
The First Stage of the problem , is to know , if the body has a Soul, which survives physical Death.
The Second stage , is to know ,if and how,the soul can acquire a New Body and take another Birth.
The third stage , is to know, if the Soul can take a succession of Births and Rebirths.
The Fourth stage , will be to know, if it is possible for the soul , to escape from the cycles of Births, Deaths and Rebirths.
The Fifth Stage , will be to know, if this soul , has Permanently escaped or Liberated, from the cycles of Births and Deaths.
The Sixth Stage , will be to know ,if this Liberated Soul, has Overcome the fear of God or Nature, from forcing it again into the cycles of Births and Deaths.
The Seventh Stage , will be to know, How this Liberated Soul , will keep itself Busy or Spend Time,till the End of the World or Pralaya