The mailed check makes me nervous that your first broker might have recorded this as a distribution instead of a rollover. If they did, you might be on the hook for a shitload of taxes. Check with them and then double-check with them to ensure the rollover is being recorded as going to another IRA and is not a taxable event. They have no way of knowing you didn't just spend the cash, so I expect trouble.
If that all works out, congratulations on your luck!