Buying a new specialization

If you are buying a new specialization, and you already have points in the base skill, does that carry over?

My friend has blaster 7D and he wants to specialize in a blaster rifle. He has Dexterity 5D. Does he get blaster: blaster rifle at 7D+1 or 5D+1? The rules seem to imply he would get it at 5D+1, but it doesn’t make sense for him to get worse at shooting blaster rifles and have to take multiple missions before it can even out. Would it be overpowered for him to take the specialization at 7D+1?