My husband has a one night stand with someone whom later got pregnant. The mother has since given up her rights to a friend. If if comes to be that my husband is the father can he sign his rights over?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

Second, ANY question on law needs to include your general locale as laws vary by area.

What makes you think the mother "gave up her rights" to a friend? She may have given the child to a friend, but unless the friend adopts the child she has probably not given up her rights. There is this myth that a parent can just sign over parental rights, but its only a myth. Only a court can terminate rights and courts are very reluctant to do so.

If the mother is allowing the friend to adopt, then the father will have to agree to the adoption. In that case, the father's rights will be terminated. Otherwise, no. If your husband is found to be the father, then he can be required to pay child support.

Your post gives us very little info to go on. Has anyone asked for a paternity test, support? Do you know for a fact what is going on with the child's custody status? You need to get your facts down pat so your know how to proceed and you need to give us more facts if you want more help.