If I enchant my companions weapon to sould trap will it capture the souls in my soul gem?

I just gave Lydia my Blackstar and soul trap weapon, she got the soultrap animation when she killed a guard, so i would say yes.

Yes, give them tons of empty gems and a soul trap weapon, bingo.

I thought all Soul Trap goes to you? not the person who has the weapon?

Soul Trapping just puts the effect on the target. When the target dies (regardless of who killed it, or how it died) you get the soul.

My Experiment with Lydia filled the Black Star she had in her inventory, when she killed a guard with my soul trap weapon.

They've filled up gems for me, so they can do it too.

Do you know if they will recharge their weapon if they got filled gems, and the weapon is depleted?

I'm using Aela for ranged support. She has a bow of flames, and it has never run out of charges? Every time I go to check her inventory the bow is at full charges. Do they even use charges?

I gave Lydia a brand new enchanted sword, and checked it after some combat, and it was about half charged.

But i just checked it again after a lot of fighting and its still half charged, so maybe not? Its a high magnitude enchanted sword with only about 100 charges.