Should I log issues with manager who is about to leave?

[Creampastry]

My manager is leaving very soon but recently I have found out he has been telling lies about my work performance and has been bullying me. Senior management are aware (I'm not the only one) but I have just seen more lies (on paper). Should I log all issues formally with HR so that the new manager doesn't get the wrong impression? Should I initiate a grievance? Doesn't seem much point as he will be gone very soon but I furious about the latest incident.

I would.

Yes, I would too

Doesn't seem much point as he will be gone very soon but I furious about the latest incident

I would definitely raise your concerns in writing, for the record.

Once he leaves, people can obviscate because he isn't there anymore

Yes from me too.

I don't think that I'd bother with a grievance, as it could be turned around that you're just being bitter and why didn't you do something about it earlier.
I would ask to meet with an HR rep or send a letter, with your viewpoints about what happened and where the soon to be ex-manager was wrong.
When the new manager arrives, I would imagine that they'll shelve all the previous manager's baggage and assess people how they find them. You have a chance for a fresh start and to show your true self and worth.
Put your energies into moving forward and don't give the stb ex manager a thought or a chance to wreck your future relationship with your new manager.
Good Luck