Is a letter from out of state considered proof of residence and, if so, how does this affect custody/divorce/deportation?

Question Details: My friend is from the UK. He and his wife are estranged and have 2 child together. He is only a registered visitor and her family sponsors him in the US. She has informed him that she wants him out by the end of the month. She says she wants him to "prove he is a good father" by moving out of state and sending her a letter. He has no job and no money. This seems like a trick to prove they don't live together and that he doesn't see his son. Am I wrong?

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