The fact of identical twins being involved in a match has no influence of the amount of matching or nature of the relationship unless the path from one person to their match includes both identical twins.
So, a case where it would matter is if each twin had a child (by different partners); then the two children, who for non-twin sibling parents would be first cousins, would show the same genetic relationship as half-siblings. This is because their twin parents have the same genes and so it is as if the two children share one parent.
It sounds as if in your friend's case the path is not believed to be through both of the twins, but just one (although the given description is not entirely clear). In that case the fact that one identical twin is in the matching path has no impact. (This is just as if the other identical twin had never been born, there would be no difference in the genes of the two matching people.)
In the case of fraternal twins, the relationships and match amounts are exactly the same as if they had simply been separately born siblings.