specific unit or specific unit-type?
specific unit can only be done if you have some way to identify the unit in the first place. e.g. the unit is preplaced on the map and so you could just throw it into a unit variable.
specific unit-type is a lot easier.
event:
[generic unit event]
a unit finishes construction
condition:
[unit-type comparision]
unit-type of constructing unit equal to <whatever>
action:
[unit - change owner]
unit - change ownership of constructed structure to <player x>