How to account for teaching work as a limited company owner – do i need to create an invoice?

Hi there
I have a VAT registered limited company and have done teaching jobs on the side in the past, usually invoicing through bullet under the business name.  They have been small payments so far and were 0% VAT.  However, they counted as income for the company and i then paid myself a salary out of them.
I have a much bigger teaching job coming up and the college are going to pay me through their payroll.  However, they have asked for an invoice.  Do i need to do this through bullet/my company or can i just send them a word doc with my rate etc?
Not sure if this is the correct forum for such a question so apologies if it is not!
Many thanks in advance.

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