Send a bill for "Consultation".
I had this done to me by the MOD some years ago. Was "selected" to tender for a job which was so poorly defined that I had to write the technical tender spec myself. They then rejected my tender but used my spec to go out to a full tender. I sent in an invoice for "Tender Specification Consultancy Fees" and they paid it
Six months later my company was awarded the contract.
I figured that, dealing with the MOD, they have no idea what they are doing and are so large that everyone assumes that some other department was handling the matter. This is a rule of thumb learned many moons ago in the RAF where many idiotic actions went unquestioned because those who would and should have asked the obvious "Why" could not bring themselves to so do in case someone of a higher rank had given the original order.
Reminds me of a story about a doctor and a lawyer talking at a party.
The doctor was complaining that when ever anyone found out what he did for a living they would ask his opinion about their latest aches and pains. The lawyer agreed that he had the same problem in that people, on hearing that he was a lawyer, would ask for legal advice. "And how do you deal with this?" asked the doctor. "Easy" said the lawyer "The day after the party I send them a bill for legal opinion". "Hey that's great" said the doctor "Thank you so much, I'll try that myself"
Two days later the doctor was surprised to receive a bill for $500 for "legal advice"