UPS also can not deliver to post boxes.
Private Mail Boxes (PMB) are generally regulated just like Post Office Boxes.
Both FedEx & UPS tell you that you can not send cash via their services.
I am surprised he wanted to use his business account.
If need be, you can have a FedEx pkg held for you at a FedEx Office (old Kinkos) or another facility.
For UPS, a package can be held at The UPS Store but often there is an additional charge if you do not have a PMB there. Charges vary from Store to Store.
If you are going to accept deposits into an account, check with your financial institution. I would ask for an account that only takes deposits and have the money swept daily into your real account. If you give out real account info, it possibly can be used to take money out of your account.
There is also Western Union, but it has some forms to fill out much of which is due to financial regulations.
One way to get around the PMB restrictions would be to rent a small space that had a mailing address.