All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The divorce that a husband sends to his wife by e-mail is a metaphor of divorce and divorce takes place only if he intended it, but if he did not intend it, then this is not a divorce (divorce does not take place).
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As regards authenticating the divorce or not authenticating it, then this does not affect divorce.
Hence, if a husband divorces his wife a revocable divorce, then each one of them inherits the other when he/she dies. But if their divorce is an irrevocable one, then they cannot inherit each other.
On the other hand, it is not permissible for a husband to claim that his marriage is still intact so that he can inherit his wife.
However, if he claims that they are still married, and there is no evidence that divorce took place, then it is his statement that should be taken into account. Ibn Qudaamah said: “If a wife claims that her husband divorced her, and he denied her statement, then it is his statement that should be taken into account, because in principle their marriage is still valid and no divorce took place, unless she has evidence, in which case, she has to provide two witnesses…”