This is the Gandalara Cycle, a series of seven fantasy books written by Randall Garrett and Vicki Ann Heydron.
Ricardo Carillo, an aging language professor with a terminal illness,
is flirting with a captivating young woman on a Mediterranean cruise
ship. They both watch with wonder, and a growing horror, as a
dazzlingly beautiful star quickly grows to engulf the sky and then
crashes into the ship.
Ricardo awakens in a blinding hot desert, with no idea where he is and
a dead man by his side.
Without knowing how or why, Ricardo finds himself inhabiting the body
of a strong, healthy, young man named Markasset. Ricardo quickly
learns that Markasset is wanted for murder and the theft of a precious
and powerful gemstone, the Ra'ira. Ricardo has only a smattering of
Markasset's memories, and no idea if he is guilty or innocent. But
with the help of a giant warcat named Keeshah, with whom he shares a
telepathic bond, and the beautiful illusionist, Tarani, Ricardo sets
out on a quest to recover the missing gemstone and clear his new name.