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I'm sure others can give you better advice than me over tourist visas (I assume that's what you are applying for?), but asking for fromal letters of invitation is all part of the visa process, there's nothing unusual in that.
They will very likely be looking for you to demonstrate that there is somewhere for her to stay (your house) and that you have a job (pimps need not apply).
I would say do what she asks and keep an eye on the process yourself, she might make a balls of it.
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