Thanks for your question. I will try to help.
She would have to apply for a standard visit visa before she travels, if she is simply coming here for a visit and then leaving.
The eligibility criteria for a visitor's visa is as follow (as I am sure you know), is that you need to show that:-
· You want to visit the UK for no more than six months;
· You intend to leave the UK at the end of your visit;
· You have enough money to support yourself during your stay in the UK without working or needing help from public funds
You have to try and show them that she has continuing obligations in her home country which will continue after the visit and therefore convince them that she is not a risk of overstay because she at present has compelling family and social/work ties to her home country which mean that she will not attempt to secure a permanent stay here whilst she is visiting. Things like a letter from her employer stating she has a job (if he does) and is expected to return to continue that job, return flight tickets, evidence of continuing accommodation (eg. tenancy agreement of evidence of ownership of a property), bank statements showing the money she has available, letters from relatives/friends confirming any obligations she has to them.
If your mother proposes to help her during the intended stay she should go to a local solicitor to draft a sponsorship declaration in which she states the terms of the visit, that she is to return at the end of it, that your mother shall accommodate her and shall pay the costs of any unforeseen expenses that should occur during her stay so that nether of you will need to access public funds. Your mother would also need to submit evidence of her ability to house her in the form of either land registry official copies confirming that she owns her own property or a tenancy agreement with a letter from the landlord confirming that they do not object to her staying for this time.
I would also consider you executing a sponsorship declaration as well in which you confirm similarly as your mother but without the part relating to accommodation and stating that although you are in a relationship you are aware that she cannot apply to to stay any longer and that it is strictly for a visit only.
This should cost around £50+vat and you can find immigration solicitors via:-
The home officer are suspicious of one party to a couple visiting the other party in the UK because of the huge problem with overstayers he so you have to give them as much documentary evidence as you can that indicates that her life remains back her home country.
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