The absorption of Buddhism into Brahminical Hinduism began after Buddhism was driven out from India. This was the result of a long drawn conflict after the death of the Buddha where Buddhists and Brahmins went into ideological conflict with one another resulting in the support of different political entities against one another.

By the time of the arrival of the Arab Muslims, Buddhism was on a decline due to a number or reasons which mostly link to the decline of political support for their position. The arrival of the Muslims had helped the Buddhists gain some traction against the Brahmins but once the Muslims had established themselves the Buddhists were ultimately sidelined and disappeared into more fertile territory such as that in China and Central Asia.

Free from one ideological opponent, Brahmins were able to absorb what they wanted into their teaching to bring the Buddhists back into the caste system.

Sources:

• India: A history by John Keay
• The Beginnings of Buddhist Art and Other Essays in Indian and Central Asian Archaeology by A. Foucher
• The History of Buddhism in India and Tibet Bu-ston and E.Obermiller