Thanks for your question.
In cases where an employee has been employed for less than a year, an employer may dismiss them for any reason whatsoever and provided that you give the employer the correct notice period and have not otherwise breached term of her contract of employment. She cannot make a claim against you for unfair dismissal if you dismiss her now.
However, by not paying her wages because of the money she owes you you have made a deduction to her wages. Such deductions are lawful if authorised by stature (none applicable to this situation) or where such a right is contained in a contract of employment or subsequently agreed in writing by the employee.
I take it none of these apply to you? If they do not then you have probably breached her employment contract by making the deduction (as unfair as it no doubt it sounds), this does not give rise to make a claim under employment legislation but she could technically make a claim for breach of contract. Even if a deduction was in theory permitted by law a deduction of the amount that would effectively mean she does not get paid would still probably be found to be fair too high to constitute a fair deduction.
You should approach the situation carefully, you can write to her giving her notice of dismissal but this may provoke her in to taking advice and then claiming for the wages. You may consider trying to manage the situation practically by contacting her to discuss amicably to gauge what her reaction is. You may then both agree to go your separate ways and you can then give her notice of dismissal and it will come as less of a surprise to her (making her less likely to claim the deducted wages).
Ultimately, it sounds as if you do not want her working for you and she does not want to work for you so it should not be too difficult to get around the problem of the deduction of wage. I think you just need some confirmation from her, so just be sensible about approaching her and hopefully you will find there is no problem.
Unless otherwise stated in her employment contract you will have to give her one weeks notice in the event that you dismiss her.
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