The Homer Impostor was hired to replace Homer while Homer was on a mysterious island. Although he has a thick German accent and has to shave his head due to not suffering from baldness, the Simpson family accepted him as the real Homer.
There was a brief moment of suspicion, when Bart commented that something was really different about him lately however, when the quick-thinking impostor replied, (in Germanic syntax) "ah, ja... I am new tie veering.." his cover was secure.
After the real Homer returns from the island by stealing a boat that Number 6 made, the two Homers fight, ending with the real Homer winning after kicking the impostor in the groin.
It is unknown what happens to the Homer Impostor afterwards.