I get how it logistically could happen, but you don't send millions of dollars out the door for anything that isn't know to the stake holders and why the money was being spent. It just doesn't work that way, particularly in that small of a firm.
Every managing partner is getting a monthly P&L and they will review the line item expenditures by account. there is no way to falsify these and not have help. The P&L has to reconcile back to the balance sheet which should be reconciled with bank balances. Someone would have to overlook massive discrepancies.
Every owner / partner / manager with P&L responsibility (if they are worth their salt) is going to review at a minimum the bottom line. They typically will also scan to compare expenditures month to month on a percentage basis to look for anomalies. It is one thing to move a few percentage points of total revenue each month, but it sounds like this guy was stealing big money.
The majority of service related companies spend money on people. Particularly a law firm, they don't buy goods (which are ripe for kick backs and other shenanigans). Their expenses are their people and consultants.
The man had help pulling this off. Someone knew and was either in on it or turned a blind eye.