Ok, so here is the problem.

I found the gun for Brotherhood of steel with veronica. And the last task in this quest is to bring it to the Brotherhood Boss (elder). So i come into his room, Veronica walks in ( slowly, direct to the boss), i see the animation of conversation but i hear no sound and my quest is UNFINISHABLE

It also happened in Camp, where i have to tell major Polalti that i did my quest, but there is no option in conversation about the end of task.

HELP MEEE

I tried dropping the gun, but it did'nt help

True, its a bit buggy. AFAIR Veronica should speak to you about it after you both leave the room, try loading the game, replaying the animation, then leave the room or even the bunker with her.

My previous save is far far away, that's a lesson for me i tried leaving bunker, room many times. Maybe there is some Save Editor? To change the status of quest?

My problem with this quest, once completed and fought the hostile bos outside the bunker. Veronica goes "whats up" and then refuse to move... she stop follow me. I can fast travel with her, and tell her to go back to the casino to wait for me.
But she refuse to move, fight or anything. Just like ED got bugged after he got upgraded, sigh...

Oh and the quest didn't want to start at all before she suddenly talked to me as we was about to blow up Vault 19.. (this after dragging her to every location that should triggered her quest)...