I usually don't jump in on grammar police threads but since this one is agonizing on, I'll go ahead and agree with Tstew and Monkeyman.
It's pretty clear if you read the sentence carefully, that "cheated on" is the verb describing what "he" did to "the woman". Your mistake was in relaying that verb action to "when he was a POW". That's not how the sentece was formed or meant to read. "stuck it out" is the only applying verb to "when he was a POW".
"cheated" had nothing to do with "when he was a POW".
I wasn't going to say anything, but it was going on for a while and appeared to be nearing blows. I just want us all to get along.
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