A guy goes into a Jewel-store owned by a logician who never lies... This is completely wrong. In classical logic that "every implication-proposition is true if its premise isn’t true" is based on the fact that there is never any change in the truth value of any proposition.
The premise in the implication-proposition in the sign is "If, at any particular time, you have given $5000 to the sales-clerk". In the scenario described, this does not have a fixed truth value, hence the application of a classical fixed truth value analysis is absurd - hence the absurd result, a result that would not hold in any court of law - for obvious reasons.
The same invalid application of classical fixed value logic to various real life scenarios that do not have fixed truth values is a common method of producing conundrums.