The reincarnation manifests himself by signs such as being familiar with the possessions of the previous Dalai Lama.

The above assumes the truth of reincarnation. I'd prefer for the article not to take a stand one way or another on reincarnation. So how about:

The people searching for the new Dalai Lama believe that the previous one will manifiest himself in the new one...

Or:

The searchers consider familiarity with the possesions, etc., as signs of the reincarnation.