This is not Popper's position. He held that observations can disprove (or undermine) a theory, but that they cannot prove a theory. Scientists will gain increased confidence in a theory that has survived many attempts at "falsification" (the term Popper used) but such confidence building results can never eliminate the possibility (or even, in any strict, calculable sense, effect the probability) that the theory in question may fail some future test. In short Popper held that there was no valid method of "verification" with respect to scientific theories.
You seem to have in mind what is often called a "crucial experiment". This is a test in which two or more competing theories make clearly different and incompatible predictions about the outcome of some experiment or observation. Assuming a number of things -- e.g. that the predictions are correctly deduced from each theory, that there are no false premises in the (inevitable) extra-theoretical assumptions implicated in these deductions, and similarly that the experimental results do not include any unrecognized artifacts -- then, yes, at least one theory (and maybe more than one!) will be "falsified," but this does not mean that the other (unfalsified) theory has been decided to be "true". It just means it has survived a test where it might have been falsified.