Quick Number Plate Retention Question

[B.J.W]

Hi, some advice appreciated here.

I've sold one of my cars a lot more quickly than anticipated - within 24 hours and to the first person who viewed it. The vehicle has a private plate (which I was going to retain, but see above).

I have the V317 form which needs to completed. Can I fill this out, send the payment, and post the V5C to the DVLA with the new keepers details included (leaving her with the V5C/2)

I am assuming that the new V5 will be sent to her, with the plate retention certificate being sent to me. The buyer has agreed to sign a letter stating that the private plate does not form part of the sale (which covers me from a legal standpoint)