Praise be to Allah.
If a man writes a clear statement of divorce in his own hand, then it does not count as a divorce unless he intended it as such, according to the majority of scholars, because writing may be subject to different interpretations.
Ibn Qudaamah (may Allaah have mercy on him) said (7/373): Divorce does not count as such without uttering the words of divorce, except in two cases:
(i)a person who is unable to speak, such as one who is mute; if he issues a divorce by means of gestures then his wife is divorced. This was the view of Maalik, al-Shaafa’i and ahsaab al-ra’y, and we do not know of anyone who disagreed with them.
(ii)if he writes the divorce – if he intended it then his wife is divorced. This is the view of al-Sha’bi, al-Nakha’i, al-Zuhri, Abu Haneefah and Maalik, and it is the stated view of the Shaafa’is.
But if he wrote it without intending to divorce her, then some scholars are of the view that it counts as such. This is the view of al-Sha’bi, al-Nakha’i, al-Zuhri and al-Hakam, because of what we mentioned.
The second view is that it only counts as such if he intended it. This is the view of Abu Haneefah and Maalik and is the stated view of al-Shaafa’i, because writing is subject to interpretation. He may have intended thereby to try out the pen, or improve his handwriting, or make his wife worried without intending divorce. End quote.
As your father did not utter the word of divorce and did not write it, rather it was written by someone else, and he signed it without intending divorce, then divorce has not taken place.
Your father’s actions have obvious negative results, including the issue of inheritance if the estate is divided by the state, because there is no inheritance between your father and your mother in this case. But if the inheritance will not be divided by the state, then the way out is for your father to bring two witnesses of good character to testify that the marriage is still in effect between him and your mother, and also broadcast that among people. Then if one of them died the other will inherit from him or her.
Another negative consequence is that if Allaah blesses him with a child from your mother, then he will not be able to register the birth, in addition to the lying and fabrication involved in his action.
As the divorce asked about does not count as such – as stated above – there is no need for him to take your mother back formally.
And Allaah knows best.