Can someone else write my son's wedding invitation? This is a woman they don't know very well.

Anyone can write a wedding invitation. There are no taboos in marriage customs. Many people invite others to write wedding invitations because their handwriting is not good, family members and even relatives and friends, or time is tight. What needs to be noted here is that after someone else has written the invitation, you should check it carefully to see if there are any omissions or mistakes so as to make up for them.