Here is how Ramcharitmanas Describes establishment of Shiva Linga by Lord Rama. The Lanka Kanda 1st Dohas Chaupai mentions:
सैल बिसाल आनि कपि देहीं। कंदुक इव नल नील ते लेहीं।।
देखि सेतु अति सुंदर रचना। बिहसि कृपानिधि बोले बचना।।
परम रम्य उत्तम यह धरनी। महिमा अमित जाइ नहिं बरनी।।
करिहउँ इहाँ संभु थापना। मोरे हृदयँ परम कलपना।।
सुनि कपीस बहु दूत पठाए। मुनिबर सकल बोलि लै आए।।
लिंग थापि बिधिवत करि पूजा। सिव समान प्रिय मोहि न दूजा।।
सिव द्रोही मम भगत कहावा। सो नर सपनेहुँ मोहि न पावा।।
संकर बिमुख भगति चह मोरी। सो नारकी मूढ़ मति थोरी।।
The monkeys brought huge mountains, which were received like playballs by Nala and Nila. When the All-merciful saw the exceedingly beautiful construction of the bridge, He smiled and observed thus: ìThis is a most delightful and excellent spot; its glory is
immeasurable and cannot be described in words. I will install (an emblem of) Lord Sambhu here: it is the crowning ambition of My heart. Hearing this the lord of the monkeys despatched a number of messengers, who invited and fetched all the great sages. Having installed an linga of Lord Shiva and worshipped It with due solemnity, He said, "No one else is so dear to Me as Shiva. An enemy of Shiva although he calls
himself a devotee of Mine, cannot attain to Me even in a dream. He who is opposed to Shankara and yet aspires for devotion to Me, is doomed to perdition, stupid and dull-witted as he is."
Then the 2nd Doha states:
संकर प्रिय मम द्रोही सिव द्रोही मम दास।
ते नर करहि कलप भरि घोर नरक महुँ बास।।2।।
Men, who, though devoted to Shankara, are hostile to Me and even so those who are enemies of Shiva but votaries of Mine shall have their abode in the most frightful hell till the end of creation.
Then the Chaupai of 2nd Doha states:
जे रामेस्वर दरसनु करिहहिं। ते तनु तजि मम लोक सिधरिहहिं।।
जो गंगाजलु आनि चढ़ाइहि। सो साजुज्य मुक्ति नर पाइहि।।
होइ अकाम जो छल तजि सेइहि। भगति मोरि तेहि संकर देइहि।।
मम कृत सेतु जो दरसनु करिही। सो बिनु श्रम भवसागर तरिही।।
राम बचन सब के जिय भाए। मुनिबर निज निज आश्रम आए।।
गिरिजा रघुपति कै यह रीती। संतत करहिं प्रनत पर प्रीती।।
बाँधा सेतु नील नल नागर। राम कृपाँ जसु भयउ उजागर।।
बूड़हिं आनहि बोरहिं जेई। भए उपल बोहित सम तेई।।
महिमा यह न जलधि कइ बरनी। पाहन गुन न कपिन्ह कइ करनी।।
They who will behold Lord Ramesvara will, on quitting the body, go direct to My sphere in heaven. And a man who takes the water of the Gangå and pours it on the Lord will attain liberation in the form of absorption into My being. Again, whosoever adores the Lord in a disinterested spirit and without guile, will be blessed by Sankara with devotion to Me. And he who sees the bridge erected by me will be able to cross the ocean of worldly existence without any exertion. Ramas words gladdened the heart of all and the great sages returned each to his own hermitage. Girijå, (says Sankara,) such is the way of the Lord of the Raghus: He ever loves those who take refuge in Him. The clever Nala and Nila constructed the bridge and by Råma's grace their renown spread far and wide. Those very rocks that not only sink themselves but cause even other things to sink alongwith them floated like so many rafts. This is, however, not ascribed to any miraculous power of the ocean, nor to a virtue of the rocks themselves, nor again to any skill of the monkeys.
You can listen audio of above verses in the beginning of Lanka Kanda here.
By the way, the mention of getting salvation through Rameshwaram Jyotirlinga is also described in Yuddha Kanda of Brahmanda Purana as I describe in my answer here.