Allocate customers' payments to account rather than invoices?

One of my customers has been sending me random bank payments with no invoice reference and I am unable to match them.  They also cannot verify which invoices relate to the payments.

What is the solution in this case?

Can I allocate the payments to invoices that are outstanding?  Do I somehow allocate to the account - which will probably mean the invoices are left "open"?

Please advise.

Thanks