This is a difficult topic. There are two separate issues here:
1. What vaccines did the child already have administered?
2. Did they provide immunity against the disease that was inteneded?
1. The answer to number one is the easier. Minnesota Department of Health has a fantastic web site where they list immunizations as they appear on international records. It is very comprehensive, but they are always interested in new additions. http://www.health.state.mn.us/divs/dpc/adps/manual/pgappend/pgunited.htm
2. The answer to number 2 is more difficult as depending on the country, some parents are told their child is being immunized and it is saline, some vaccines have not been stored correctly and were ineffective, some were given too early (child too young) to provide immunity, etc etc. I have a student who was adopted from an Eastern European Orphanage and was supposedly immunized fully. His physician ran titers and there were no anitbodies for some of the diseases and very low titers for others and the physician is redoing the whole series. It is dependent on the country the child came from, the level of health care. Even then some physicians choose to readminister the vaccines rather that go through the cost and bother of the titers.