The question is
how did this movement (Vegetarianism) spread to Hinduism?
Ramayana says (Kishkinda Kanda)
पंच पंच नखा भक्ष्या ब्रह्म क्षत्रेण राघव | शल्यकः श्वाविधो गोधा शशः
कूर्मः च पंचमः || १-१७-३९
"Raghava, five kinds of five-nailed animals,
viz., a kind of wild rodent, a kind of wild-boar, a kind of lizard, a
hare and fifthly the ...
What is influence of Jainism and Buddhism in introducing Vegetarianism to Hinduism?
Vegetarianism was already a part of Hinduism, and Jainism and Buddhism are religions founded based on Hinduism.
The fact is, according to Hinduism, meat can be eaten only if the animal is sacrificed in a Vedic yajna:
5.31 - ‘The eating of meat for sacrifices’—this is ...
Actually this was the motive of there incarnation to create a fake religion. In kaliyug, asuras started following Vedas but still they spread terror. As they were following path of Vedas, Deva couldn't defeat them. That's why Vishnu incarnated as budha to take them away from Vedas by making another religion.
Padma Purana VI.252.108-115
“…The glorious one, ...
Yes. Budha was Vishnu avatar. There are many budhists oppose this claim but many great budhists personality accepted the truth.
Thomas William Rhys Davids (Founder of Pali taxt society)
Budhism p 116-117:- "We should never forget that Budha was born and brought up a Hindu and lived and died a Hindu..........he was the greatest and wisest among Hindus."