It is not permissible to do hair transplants for the beard unless that is for the purpose of treating a problem and removing a defect, such as if it was lost or there was some deformity because of sickness or burns, for example. That is because transplanting hair for the beard for purposes other than these comes under the heading of changing the creation of Allah. 

Evidence for the permissibility of using cosmetic means to remove or correct an acquired defect is to be found in the report narrated by Abu Dawood (4232), at-Tirmidhi (1770) and an-Nasaa’i (5161) from ‘Abd ar-Rahmaan ibn Tarafah who said that his grandfather ‘Arfajah ibn As‘ad’s nose was cut off on the day of (the Battle of) al-Kulaab, and he wore a nose made of silver, but it began to stink, so the Prophet (blessings and peace of Allah be upon him) told him to get a nose made of gold. 

The hadeeth was classed as hasan by al-Albaani in Saheeh Abi Dawood. 

Dr. Saalih ibn Muhammad al-Fawzaan (may Allah preserve him) said: It seems to me that there are two scenarios with regard to the beard: 

1.

The first scenario is where the growth is naturally sparse, in which case it is not permissible to increase it by means of hair transplants for the following reasons: 

(i)What is meant by the command to let the beard grow is to leave the beard alone and not remove anything from it by cutting or shaving. There is nothing in that command to indicate that it is prescribed to increase it by means of hair transplants, and by analogy it is not prescribed to increase it by means of remedies. In fact it is more likely that transplants are not allowed because of the side-effects and complications to which that may lead.

(ii)Doing hair transplants for the beard when there is no need to do so comes under the heading of changing the creation of Allah, may He be exalted. Simply wanting to look more handsome or to look a certain way is not sufficient to make this change permissible. Moreover, it involves surgery and exposing oneself to side-effects and complications of this surgical procedure.

2.

The second scenario is where the hair of the beard does not increase or it falls out because of sickness or an accident. In this case it seems to me – and Allah knows best – that it is permissible to do a hair transplant for the beard, because this comes under the heading of medical treatment and removing defects, especially if that sickness or accident has left the man looking deformed.

End quote from al-Jarraahah at-Tajmeeliyyah, p. 159 

And Allah knows best.