Moving in with parents is best described as change of circumstances rather than cohabitation. My ex moved in with her parents when she left me, and collected alimony. When she moved her boyfriend into the basement with her I was ready for legal action, but she got married, and that's all she wrote.
Hope her parents are enjoying it, they now have my 2 kids, her new baby, and her husband's kid. Party of 6 in the basement

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conclusion: file for modification based on change in circumstnaces