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Provided you are both in agreement to this, and you are trusting of her, there is no real issue in you doing this.
You will, however, need to get a Deed drawn up by a Solicitor to show the change in percentage ownership and the Deed should also confirm the amount you are paying to her in consideration of you receiving 99% in the property.
The only thing you need to be made aware of is that as she would remain a legal owner, she would be entitled to occupy the property at any time in the future. I am sure she would not want to do this on a practical level, but legally, she would be entitled to!
Free advice- The only downside from her point of view is that she would of course remain on the Mortgage, meaning she is as legally responsible for the payments as you, and while the Mortgage remains in your joint names, it will mean she will find it hard to secure any other Mortgage in her sole name.
I hope this assists you and sets out the legal position.