Playing Boggle and other board games can be incredibly fun, exhilarating, and sometimes quite competitive. This type of situation does at some point or other inevitably lead to one of the players trying to cheat, subtly or otherwise. In Boggle, it can be as simple as pretending you found a word that you didn't, or as intangible as a Boggle player insisting on the validity of slang words or foreign words as acceptable Boggle words.
Whatever it is, cheating in Boggle becomes a problem as soon as it starts bothering one or the other of the Boggle players. Here are some approaches for dealing with Boggle cheating.
Read our article on how to decide which words are valid for Boggle play. Then discuss with your Boggle group (including the cheater) exactly which strictness level is best for your Boggle playing. The stricter the Boggle game style, the harder it will be for the cheating player to justify his iffy words. Even if the players decide upon a looser version of playing Boggle, at least the play style will be clearly defined. This should make it easier to enforce the rules on all Boggle players.
If a clearly defined style of Boggle play does not alleviate the cheating problem, talk to the other non-cheating Boggle players privately to see if they agree that the cheating is a problem. Assuming they agree, you should plan to have one of you talk to the Boggle cheater privately. You don't want the Boggle player to feel like he's under attack.
Explain concretely what they do that bothers the rest of the Boggle group. Cite specific examples if you can. It's possible that the Boggle player may not even realize he was stretching the rules that much. And if he did know, being directly asked about it may shame him into mending his cheating ways when playing Boggle.
Unless your Boggle group is actually willing to kick the cheater out of future Boggle play (which assumes that this person isn't a family member or friend!), if the other methods fail you may just have to let it go. No one likes a cheater, particularly if you play a competitive Boggle game, but it is a game after all.
If nothing else works to quell the Boggle cheater, you might have to be the better Boggle player and person and just stop fighting. Just focus on your own Boggle playing and ignore the cheater. It's more important to have fun and enjoy each other's company than to play a perfect Boggle game.