Divorce (talaaq) counts as such even if it is not registered in court
Question

                Does a Muslim divorce have to be registered legally as in other religions?.
Praise be to Allah.It is not essential for 
    divorce to be written down or recorded; divorce takes place as soon as the 
    words are uttered. So if a man said to his wife, “You are divorced” or he 
    says, if she is absent, “She is divorced” or “I have divorced her” and 
    similar phrases, then it counts as a divorce. It is not essential that it be 
    witnessed or that it be done in court or in front of the wife. 
Recording the divorce and 
    proving it in court is the correct action, so as to protect people’s rights 
    and prevent tampering with the limits set by Allah, especially if it is an 
    irrevocable divorce, such as if he has divorced her three times. In that 
    case, the sharee‘ah court has to be notified of that and issue 
    documentation, so that the woman who has been divorced can remarry if she 
    wants to, and so that the husband’s rights will be protected and the 
    divorced wife will not ask for maintenance after an irrevocable divorce. 
To sum up: divorce takes 
    place once it is uttered or written with the intention of divorce. As for 
    recording it and documenting it, this is to protect rights and is not a 
    condition of divorce taking place. 
And Allah knows best.