He authorized her to get divorced and she got divorced herself

If the husband says to his wife: Divorce yourself, or It’s up to you, or You choose, or I authorize you to get divorced, and she says, I divorce myself, then it counts as a divorce. 

The fuqaha’ discussed in detail a number of divorces that the wife may do, depending on the phrase used by the husband, but as the wife only issued one divorce to herself, there is no need to go into those details here. 

Based on that, one divorce takes place if the wife says “I divorce myself from you” and it cannot be accepted from her that she did not intend a divorce, because if divorce is mentioned clearly, then the one who issued it is not to be asked about his intention, and the divorce counts as such even if he says I did not intend it. 

If this was a first or second divorce, then you may take her back so long as the ‘iddah has not yet ended. 

The wife has to understand that divorce is a serious issue, and that there is no room for joking or playing about in this matter. It counts as a divorce whether it is issued in earnest or in jest, as the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “There are three matters in which seriousness is serious and joking is serious: marriage, divorce and taking back (one’s wife).” Narrated by Abu Dawood (2194), al-Tirmidhi (1184) and Ibn Majaah (2039); classed as hasan by al-Haafiz Ibn Hajar in al-Talkhees al-Habeer (3/424) and by al-Albaani in Saheeh Sunan al-Tirmidhi (944). 

It is not permissible for a woman to ask her husband for a divorce unless there is a reason which makes it permissible for her to do so, such as bad treatment. See the answer to question no. 117185. 

See also the issue of Tafweed al-Talaaq (delegating divorce) in al-Mawsoo’ah al-Fiqhiyyah (13/113) and al-Sharh al-Mumti’ (13/84). 

And Allaah knows best.