All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
You did not mention to us what you meant by the fact that this man had cheated on his wife, as this term may be used by some to refer to a man’s marriage to a second wife, while others may use it to refer to an emotional relationship with another woman. If the first meaning is what is intended, then he does not have the right to desert him just because of this reason. He only did what was legally permissible.
And if the latter meaning is the intended one, then there are only two scenarios:
The first: that he has repented from this sin, in which case it is not permissible to desert him, as the one who repents from sin is like the one who has no sin.
The second: If he persists in this sin, then deserting him is permissible according to the Sharee’ah, but it is necessary to take into consideration the interest (welfare or benefit) in that, so he should not desert him if he fears that it would lead to a detriment or harm.
Allah knows best.