Invoicing while full-time employed

I'd need some help in understanding what I need to do, admittedly I am getting into this for the first time.
I am full-time employed in a privately held company in the UK. Recently, I started doing some work (in the 'spare' time, e.g. evenings and weekends) to help my girlfriend out with some things she would not know how to do. My original idea was just to help out, but now her company wants to pay me for my work and asked me whether I can 'invoice'.

I have been checking the HMR website for advice, but could not find anything. My questions are, and apologies for them being so trivial:
- what exactly means 'invoicing'?
- what does it involve?
- Can I 'invoice' while a full-time employee at a company?
- Supposing the above is possible, what would I need to do?

Sorry for the many questions, and thanks in advance for your help.

Regards.

An invoice is a bill; if someone asks you if you can invoice them, they're asking you if you can send them a bill that they can pay.

If you're an individual in the UK, to invoice someone, you generally need to be registered as self-employed with the Revenue. This doesn't change your normal employment status -- that is, your normal job is unaffected -- but it does mean that you'll need to fill in a personal self-assessment tax return every year (if you don't already). On the tax return, you'll need to declare how much you invoiced over the year, and then you'll be charged income tax on the money you earned.

The question, whether you can invoice, means: "Are you registered as a company or a sole proprietor so you can issue an invoice?" In some countries you can issue invoices also as an individual, but I don't know if you can do this in UK.

When a company A buys services/products from company B, then company B issues an invoice and company A makes payment based on this invoice. Invoice is being keeped in the books in case inspectors come in and ask why this payment has been made. On invoice the taxes are stated which must be payed.

When a company is doing business with individuals (not registered companies), whey can pay you a salary (if you are employed there) or as a temporary worker. Ask them if they can pay you as a temp worker. (Maybe you will need to sign a contract for temporary work.)

Another option is that they pay to your girlfriend as additional bonus to usual salary.

If you would do more business like this, register a LLC company in UK and pay about 500 GBP/year for an accountant (for minimal bookkeeping). Registering a company in UK will cost you less than 50 GBP.