Translation:My friend finished his studies.
It's not it was simply not included in the accepted translations. My apologies. I've added it and many thanks for reporting it.
Can we omit του at the end of the sentence, and still have the same meaning? (and a syntactically correct sentence)
It would be the same as saying "my friends finished the studies". Weird to say...
In English it's definitely a no-go, but does it work in Greek? I know a few other languages in which it does work.
Thinking it over, it is ok to say it, just not so common (for me at least)