What is the ruling regarding a non-Muslim couple who entered a marriage invalid in Islam (e.g., combining two sisters, marrying ten women, or marrying a woman observing 'Iddah or apostate), who subsequently embrace Islam after a triple divorce?

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The couple is not permitted to resume their marriage. This ruling is based on the principle that if we validate their internal legal acts regarding marriage, we must similarly validate their pronouncements regarding divorce. Consequently, the man may retain the second of the two sisters or the fifth woman he married contractually.