When is the birthday of a ger?
Although a Ger is considered to be “born anew” when becoming Jewish, this is a halachic concept that relates to family relationship and the like, and it is not a “biological fact.”
The Ger’s birthday thus remains the date that he was physically born on.
Note that there is no actual halachic significance to a person’s birthday, other than determining his age, which is important only for a bar or bat-mitzvah. For this purpose the date of birth is of course the “birthday.”