back to the future
There is an extremely popular '80s movie that eponymously coined that ostensibly oxymoronic expression. That movie is Back to the Future, the plot of which involves the protagonist, Marty McFly, being sent back in time, getting trapped there because the time machine runs out of power upon arrival, and then trying to work out returning to his "original time," as you put it, while also trying to head off an existential crisis created by his trip back in time.
How you would use that phrase in your example would be:
"He was able to go back in time, but he couldn't go back to the
future."
Another possibility that has a somewhat different effect would be:
"He was able to go back in time, but he couldn't get back to the
future."
Because of the movie Back to the Future, if you were to say either of those, "go" being the verb used in the movie but "get" maybe conveying a bit more clarity, like for someone who on the off chance hasn't seen or heard of that movie, you could rely on it being understood that he couldn't get back to his "original time."
It's increasingly common that expressions are coined in major motion pictures because so many people see them that it creates an almost instantaneous common basis for widespread understanding. An early example of this is found in the English verb "gaslight," meaning "to cause someone to doubt his or her sanity through the use of psychological manipulation," originating from the 1944 movie named, you guessed it, Gaslight, the plot for which involves a man seducing a woman and tricking her into marrying him and then methodically brainwashing her into believing she is seeing people and things that aren't really there and that she's gone crazy so that he can search for and steal treasure that she doesn't know is hidden somewhere in her very large house, a house she inherits at the very start of the movie.