As Dick Foran and Wallace Ford put the torch to Kharis the Mummy in The Mummy's Hand there's no way that Universal Pictures was thinking about a sequel. Otherwise they would have made sure to identify the fact that the action was taking place in 1912 and had everyone wear costumes of the period.
So it looks a little ridiculous to have Dick Foran and Wallace Ford now elderly beginning The Mummy's Tomb made up as elderly gents with Foran reminiscing about those days on that dig in Egypt where he bested the cult of Kharis and Princess Ananka and brought back the Princess Ananka's mummy with the treasures of her tomb. The first 10 to 12 minutes of this film is a flashback synopsis of the previous film.
But it turns out that Wallace Ford didn't really kill George Zucco with those bullets fired at point blank range. George has been waiting for 30 years, but he and the cult want some payback. Kharis survived too and Zucco before he dies turns him over to a new handler in Turhan Bey. They've even got a cover story with Bey getting a job as cemetery worker, the better to bring Kharis over from Egypt.
The Mummy's Tomb takes the unusual step of having Kharis kill the heroes of the previous film. But Foran left a grown son in John Hubbard who has taken up the fight against the undead. And Bey deviates from the mission because he's decided he wants Hubbard's intended bride Elysse Knox all for himself and he sends Kharis out to arrange it in his inimitable fashion.
I think you see where this one is going, but Universal did this one in their usual Gothic horror style. But The Mummy's Tomb is not as good as its predecessor and none of those films involving Kharis are anything approaching light years as good as Boris Karloff in the original The Mummy. Universal did not do as good as it did with Dracula, Frankenstein, and The Wolfman.
Mummy films are the runt of Universal's litter.
