Weird one. Finance Company & VAT

Client purchases a machine from Belgium circa £40k (paid in Euros).

No vat on invoice - correct.

Client aproaches Finance Company (major bank) and they provided a VAT invoice for £40k + £7k vat @ 17.5%

There is a summary showing Total due           £47000

less deposit                                                  £17000

Total finance                                                 £30000

Client receives £30000 from finance company and is repaying in accordance with the agreement.

I have just spoken to the finance company because I could not understand the £17k "deposit".

The answer was that the deal was in the nature of a "letter of intent" and the deposit would have been paid to the overseas supplier.

When I asked how they could invoice my client for equipment they did not own they said "we have an invoice from client for £30k"

Next question was "is there vat on the invoice?" to which the answer was "no just £30k"

So am I missing something here?

On the face of it the finance company have lent £30k to be repaid with interest.
They have purchased a piece of equipment for £30k and sold it for £40k and have (presumably paid over £7k in VAT. But how on earth do their books balance?

My client has not recorded anything other than the original purchase and the £30k finance in and repayments out. So net his figures are right.
However surely he needs to raise a vat invoice for the sale to the finance company (but in what amount?) and put through the purchase and claim the £7k back.

Sorry it's so long.

EDIT:

Finally assuming the paperwork is correct what is the correct way to deal with the sale/purchase?

Do you have a sale of the asset purchased with loss or profit on disposal and a subsequent purchase at another figure? Or is it correct just to deal with the vat and introduce the finance?