They do not need to be converted back to Buddhism. All they need to do is revive back their practices in Buddhism.
They cannot revive the Buddhist practices of their ancestors without taking Buddhist vows, which is a case of what is called “conversion”.
No one is born a Buddhist. One needs to take Buddhist vows in order to become one.
Jews and Hindus believe that they, and only they, are born Jews or Hindus. But these are non-Buddhist beliefs, which are at the very basis of their respective narcissistic, racist, exclusivistic ideologies.
Islam, on the other hand, believes that everyone is born a Muslim, and therefore that acceptance of Islam is a mere reversal to one's “original condition”.
Funny enough, this makes the Dzogchen ideology, which preaches a “return” to an “original state” somehow akin to Islam. This might point to the non-Buddhist, Manichaean, even Zoroastrian, roots of both Islam and Dzogchen (both Bön and Nyingma).
For Buddhists, on the other hand, there is no original state for beings in samsara except for the root afflictive mind, ignorance. Therefore, one needs to
get rid of such an original state, not to return to it, in order to achieve liberation and enlightenment.
Believing in such an “original state”, as Muslims and Dzogchenpas believe, implies rejecting the stages of the path, the essence of the teachings of Buddha Shakyamuni, and of his foremost expounder, the Second Buddha, Manjushri Je Tsongkhapa.
Therefore, it comes as no surprise that the Muslim Dalai is also an enthusiastic Dzogchen practitioner, and is always intent on destroying the pure Buddhist, Gelugpa tradition of Je Tsongkhapa.