If they are trying to just store their cash, and have no desire to recover it except by showing up where they deposited it, then they don't need to carry a document with them - they'd only need such a document at the time of withdrawal. Bank the cash, stow the document somewhere (or with someone) safe and reliable, and pick it up when you need it.
Since they probably deal face-to-face with the banker, they probably don't even strictly need the document. They are violent hero types, and the banker is probably not going to shaft them unless he feels extremely physically secure from retribution. A verbal agreement may be all that's required.
Nod. Verbal agreement with whoever is storing the loot is how I've done it. So far, the PC's have used a priest of St. Cuthbert in the Keep on the Borderlands, and the church of St. Cuthbert in the capital city where they spend most of their time. They figure LG clerics are trustworthy, and the PC cleric of that religion is the go-between. No need for the PC's to carry records -- the church has its own records and remembers who they are.
Theoretically, they could also have banked with a dwarven jeweler in the capital, or with a dwarven moneychanger/loan shark who has a fortified home near a minor dungeon.
In all cases, it would be a matter of honor and verbal agreements, and only recoverable from the person who was holding onto it for you. The idea of passbooks and so forth would be alien to the nature of the deal, making it too transactional and formal. It's more like petsitting than actual banking.
Oh, also, one of the PC's bought a bar inside the Keep on the Borderlands when she retired from the party . . . a more liquid, yet less easily liquidated, investment.
If they wish to access their money on the road, they need to use a commonly accepted form of documentation.
IMC, I suppose that might be possible using an multinational organization like a Church or the Greyhawk Thieves' Guild, with long advance notice.
But to bring wealth on the road, the usual means are Portable Hole/Bag of Holding, and/or gems.
In one case (at 2nd level), they did have a written document from the ruler, entitling them to stay at inns, and board their horses and themselves as feudal dues. But that's chump change stuff to higher level adventurers.
