Invoicing old lecturing services through a new Ltd company

I've been working in the last few months, but running late in creating the Ltd company, sending invoices and getting paid. My customers are aware that I'm planning to invoice them through the Ltd company.
Some of the work is totally done, some others are still not over (e.g. task 1 done, but task 2 will be done in the following days).

Can I create my Ltd company today, then prepare the invoices (invoice date will be after the company creation, but the service item date will be somewhere in the last 6 months) and send them out so I can get paid?

I have something like 10 invoices to send out for a total of 10k maybe.

 

A limited company can't invoice for something that happened before it was registered.