After a horrible accident Jack a loving husband and father awakens in hospital with anmesia, sitting next to him is a woman who is not his wife but she convinces him otherwise.

That exactly why "Unknown" work, instead of an amnesic trying to recover his memory with external help, the hero never lost his memory despite everybody trying to convince him that he is crazy.
If he going to receive an inheritance, maybe they are trying to swindle him of his money with an actor taking his place. Maybe he read about the inheritance in the media, when doing research on himself.
But again to do research on himself he needs to know who he is.
The only way your amnesia would work is if he was the double of a rich/influential/important guy and that they uses him as a patsy for their scheme. He play the other guy when they rob, spy him and then kill him. However in the mean somebody that he loves is in danger and he wants no part of that scheme.
Maybe his daughter needs a kidney transplant and he had been kidnapped before the operation. Now he has to race across time to find his daughter and extirpate himself from the con.

>> he has an ID on him

Which enables them to contact his real wife and children. End of story.

(If the story is set anywhere near the present tense, it's set in a Big Brother world of electronic surveillance and massive aggregation of personal data such that it's now harder than ever to lose one's identity, to drop out of sight.)

I would assume he has an ID on him and he is told he in about to inherit.

I agree that a particular problem (like amnesia) should lead to a specific problem to solve, question to answer, but...

If the guy wakes up with amnesia, by definition,he's forgotten his past. How does he know he's going to collect an inheritance?

What's that you say? A friend knows and tells him. Well, If he has a friend close enough to know that he has an inheritance coming, the friend would surely know if he's married. And if married, would be able to ID the wife.

Once again, the woman is exposed as an imposter. End of story. The devil is in the details in making a Hollywood Amnesia story believable. Doctors dubbing authentic amnesia as "Hollywood Amnesia" is an inside medical joke on how absurd and implausible Hollywood amnesia stories are.

I have noticed that some loglines on this site have a tendency to describe a scene instead of a story.

A guy wakes up with amnesia to a woman claiming to be his wife is a scene.

What does you character want
What is standing in his way.

This will be different from your story but how about this as an example:
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"After waking with amnesia a loving father has three days to investigate whether the woman claiming to be his wife truly is or is she and imposter after the inheritance he's about to receive."
-----

See, now in the logline he has a goal, he must discover whether the woman claiming to be his wife truly is his wife. There are also consequences. If she is a phony she may steal a large inheritance he's about to receive.

In your logline re-write, ask what the character has to 'do' during the story.
Ask what's standing in his way?
Are there any stakes involved?
Is there any irony?
If so try adding those elements to your logline in a concise manner will improve your logline greatly.

Hope that helped, good luck with this!

One problem with the logline as currently written is that if he is a "loving husband and father" then he has a wife and at least one child -- people who know who he is (or was), who would be ready, willing and able to expose the other woman as a fraud. End of story.

Unless...

Thanks for the clarification

True, there is a lot of anmesia stories out there and I am trying to make it different (even if its only a slight difference) from the others. It's still on the first draft, so things can change as I continue to write.

just a typo ment husband