If the cat has had recurring UTIs and every single time, the vet gave
amoxicillin for a ten-day period in a certain dose, and last week when the poster's little son got an infection the doctor prescribed amoxicillin and lo and behold it was the same stuff, and there was a lot left over, and now the cat has a UTI again, I might chance it. But otherwise, no. Too easy to miss one's guess about what is wrong and about what would fix it.