Is the wife's return after three years of her divorce—one pronouncement of divorce, during which her husband deserted her, yet they lived in the same house—considered a valid return, and what are its implications, especially since the wife intends to file for divorce?

If the waiting period (iddah) has ended and the husband has not taken his wife back, she becomes irrevocably divorced from him (baa'inah). She cannot return to him except through a new marriage contract (aqd jadid) that fulfills the conditions of marriage, including a guardian (wali) and witnesses. Her return to him without a new contract is invalid, and she must separate from him. This separation does not require a divorce.