> I find it suspicious that there is no record of me handing in the money and am thinking of writing to the manager
Yes, you definitely should. It would be useful for them to know that they possibly/probably have some dishonest staff in their store.
You need not worry about anybody losing their job for this. Nobody is going to lose their job, because there's no evidence of anything. The fact there's no evidence is part of the problem that the store has.
The store manager needs to take a look at their processes. For example, as VHG suggests, using a "mystery shopper" to hand in money, see if they're given a receipt and seeing whether anybody claims it might make people think twice about pocketing cash that doesn't belong to them. Your letter could prompt the store manager to put this system in place (or remind them that it already should be!).