Since the service organization is a non-customer and we would have no way of knowing which individuals are authorized to act on their behalf, we would issue a bank check, payable to the organization. Even if the org was a customer, I prefer my staff to issue the check - that way we never find ourselves in the middle of an internal organization squabble - the good old Cover Your Assets (CYA) rule of banking!
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My comments are absolutely no reflection of, nor influenced by, my employer - take them at your own risk.