Most people won't do that because the spell can be used to track you, so you end up having to really trust the other guy, but yes you can cast on others.
There's also the issue of quickening being technically permanent, but in practice hardly so. Dispelling is hella easy in this edition. Yes, you can spend karma to make dispelling harder, but that's not the only concern: mana barriers. Mundanes are likely to not even notice them, but they'll potentially scoop your spell right off (irrespective of the karma you spent to "toughen" it up) and kick off an astral alarm to boot.
Then there's also the possibility of an astral security guy simply requiring you to drop your spells or leave. Since the mundane can't drop your quickened spell, the face with Increased Charisma may not even be allowed in to the mob boss' office at all.
