If she beats him he'll claim she

The Cambridge Grammar of the English Language by H&P (Page 126) has this example of non-deictic past:

If she beats him he’ll claim she cheated.

CaGEL explains this sentence as follows:

The time of the (possible) cheating is not anterior to the time of my uttering [the sentence], but to the time of his (possibly) making a claim of cheating.

Can we change past cheated to present perfect has cheated?

If she beats him he’ll claim she has cheated.

Is there’s any difference in meaning?