As most folk know .. mine was a "professional" install as against a DIY and came with the full (original type) certificate .. I still have it ..
DVLA were not interested in that certificate in any way, shape or form. They wanted proof of conversion and a copy of the garage invoice was what they wanted.
Once DVLA were happy the V5C (and all on-line data) changed to "Bi-Fuel" ... and this is all that every insurance company I have asked for a quote has ever needed .. I have more problems with the body kit than I do with LPG regarding insurance.
The ONLY time a copy of that certificate has ever been needed was when I checked the new database and the car was not on it.... they then wanted the original certificate ... they got a copy and a snotty letter. I then got a letter from the installers apologising for the problem .. they had sent the details in 8 months before.... but the prats running the database had not got around to entering them !!
So, in summary .. the database, and the company running it, is a self -serving, profit making, job protection unit that does nothing but allow cowboy companies to pretend to be government authorised .. when they are absolutely not.