Complex sentence: However, the problem with her statement regarding the unknown birth date of Oliver L. Roberts is that Brushy Bill claimed that Oliver P. had been his distant cousin, and after Oliver P. died, he had assumed his deceased cousin's identity.
Split into simpler sentences: However, the problem with her statement regarding the unknown birth date of Ollie L. Roberts is that Brushy Bill had disclosed that Oliver P. Roberts had been his distant cousin. After Oliver P. died, Brushy Bill says that he had assumed his deceased cousin's identity.