As T74 told you, there is a residency requirement on his part before he can apply for citizenship.
Further, LPR status is not some convenience you get if you don't intend to reside in the US. It will not be issued, nor can it be maintained, if you do not reside in the US (subject to permitted absences abroad).
As for your child, depending on the timing they may or may not already have US citizenship. You may wish to consult an attorney on that issue.