Thanks for your question.
A letter of invitation is fine, but sponsorship declarations are better. You should ask a local immigration solicitor to draft one for your and one for your mother.
This is a statutory declaration in which you should state:-
1. who the person making the declaration is
2. that they invite the person to come here
3. that it is intended that she will return home after her stay here
4. that you undertake to cover the costs of their return passage home if necessary
5. that you undertake to maintain the costs of her visit here without accessing public funds.
6. that you (or your mother) own/rent your own home and undertake to allow her to reside her during the time of her stay.
These are sworn in front of a solicitor. They can then be sent to your girlfriend to submit with her application. It should cost around £75.00 in total for both.
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