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Packmule dev here - thanks for the thumbs up. Packmule is the same experience on both the extension as the mobile app but I focus development on the mobile app.
I use Packmule for Destiny on Android, works a treat and lets you move and equip items from anywhere to anywhere, none of this moving stuff to the vault changing character, then moving them back out again, just done in one command.
You should check out these two Chrome Extensions and one of them has an Android app:
Destiny Item Manager
Packmule for Destiny
Packmule for Destiny for Android
Although i really like the app it has a a lot of UX problems thus I prefer packmule.io
it offers authentication directly through sony. (security+) and the dev also has a android application out. and since i mostly use my smartphone to quickly switch gear around this comes really handy.
the android app can be found in the store: packmule.io for android
not to bash any of both devs, I think both are a gem for our community and I am thankful for their effort.