Koi talaq potito hoyese.

Wa Alaikumus Salam Wa Rahmatullahi Wa Barakatuhu,

I apologize, but I am unable to provide a complete and accurate answer to your question because the description of the situation is not entirely clear. However, I will do my best to explain the Islamic ruling based on the details provided.

Summary of the situation as I understand it:

1. A husband sent a written notice of one (1) Talaq (divorce) to his wife.
2. One month later, a Khula (divorce initiated by the wife in exchange for compensation) was conducted.
3. Both parties signed the Khula documents.
4. Nothing was spoken verbally (no verbal divorce).
5. The question is: Can the same couple remarry after the wife completes her Iddah (waiting period)?

The Ruling:

1. Regarding the written notice of Talaq: In Hanafi Fiqh, if a husband writes a clear and explicit word of divorce (like "Talaq") to his wife with the intention of divorce, one Talaq (Raj'i - revocable) takes place. Since the notice was sent and received, and it was an explicit written divorce, one Talaq Bainuna Sughra (minor separation) occurs if the wife was in a state of purity (Tuhr) during which they had no sexual relations. If the conditions were not met, it could still be counted as one Talaq.

2. Regarding the Khula one month later: If the first Talaq had already taken place via the written notice, then the subsequent Khula would be invalid because the marriage had already been dissolved by the first Talaq. However, if the first Talaq was Raj'i (revocable) and they were still within the Iddah period, the Khula would finalize the separation. In any case, the marriage is now dissolved.

3. Can they remarry?

• If one Talaq was given (whether by notice or Khula), the couple can remarry with a new Nikah and a new Mahr, provided the wife completes her Iddah (three menstrual cycles or three months if not menstruating) from the date of the first Talaq.
• Since the Khula was done one month after the notice, and the Iddah must be completed from the date of the first Talaq, they must wait until the full Iddah is over before remarrying.

Important Note: If the husband had given three Talaqs in the notice, then remarriage between them would be permanently forbidden unless the wife marries another man, consummates that marriage, and then gets divorced (Halala). However, based on your statement that it was "1 vain talak" (one Talaq), this does not apply.

Final Answer:

Yes, if only one Talaq was given (via the written notice or Khula), the same couple can remarry after the wife completes her Iddah (three menstrual cycles). A fresh Nikah with a new Mahr and two witnesses will be required.

However, if the written notice contained three Talaqs, then they cannot remarry each other without Halala, which is strictly prohibited in Islam.

References:

• Radd al-Muhtar (Ibn Abidin): Vol. 3, Kitab al-Talaq – Details on written divorce and Khula.
• Fatawa Alamgiri: Vol. 1, Kitab al-Talaq – Conditions for Talaq via writing.
• Al-Hidayah: Kitab al-Talaq – Rulings on revocable divorce and remarriage.