I found a great app just now, just go to play store if you're on Android and get "Tower Ghost" for Destiny. It's apparently a fork of Destiny Item Manager (DIM). I think it has iOS, Chrome, and Firefox versions too.
I bought a little 199 Samsung 8" tablet a few weeks ago, partly to aid playing Destiny. But really it hasn't helped that much. It was still much easier to go in the other room and transfer items via my PC than the somewhat cumbersome Destiny app for Android. Which was only really worth bothering with if I say needed just one gun.
However this app really hits the spot, it makes transferring (multiple) items and weapons (mainly) between characters and the vault on a tablet a breeze, well so far I just only started using it. But I already love it. It is supposedly for phones too but I haven't tried that. Like literally all your guns are laid out in front of you and you just chose where to put it, vault or any character, without the intermediate step of moving it to the vault (just like DIM in that respect)
https://play.google.com/store/apps/details?id=com.richardpinedo.towerghostfordestiny
Those look like phone screens, on my tablet it's actually far better as it appears all characters and the vault are onscreen at once. This is like almost what I've been dreaming of in terms of a tablet app. With the caveat I have not used it a lot yet.
Edit: Here's a screen shot from my tablet
you just touch any gun and choose whether to store or equip it on any character or put it in vault if it's not already. Like say I touch vex mythoclast this comes up.
So you just pick the icon of the character you wish to store or equip it on (of course you only have equip option on the character it's already stored on). Amazingly good design. Pretty similar to DIM for Chrome but on a tablet app.
I'm a little scared of these types of apps after that lost weapon scare recently, but it turned out fine. And they all claim the risk with any app is no more or less than it is with Destiny's official app. I read a comment on Destiny that said just dont transfer a weapon (using any app) during a "transition" screen, which he said was like the momentary black screen when you go from orbit to tower or when you die. Have no idea if that's nonsense, but it's probably a good idea to make sure you are firmly somewhere before transferring.