My mother will be entitled to both personal allowances ie £650,000 when she dies and she has given away about £500,000 mostly within the last three years. Will her threshold for gifts be £325k or £650k? Or does it matter?
This is actually a very good question.
I am assuming that what you mean is that your father died and passed his estate to your mother. As a result his inheritance tax threshold (IHT) was unused, as transfers between spouses are exempt from IHT. Under current rules your mother can inherit your father's unused IHT threshold s doubling her allowance to £650,000 (from the usual £325,000).
However, your mother will not inherit your father's threshold until her death. So technically gifts and lifetime transfer are assessed against her single allowance (currently £325,000). It is only death that her Inheritance tax threshold will increase.
In reality if she has made a number of Potentially Exempt Transfer (PETs) such as cash gifts to people then IHT would only be payable on her death, so her higher threshold would apply. The problem comes when she has made (or makes) chargeable lifetime transfer (such as gifts into trusts) which attract 20% inheritance tax at the time of the transfer. Unfortunately. this charge is based on an IHT threshold of £325,000 and the tax paid is not recoverable upon her death despite her inheriting your father's IHT threshold.
On the plus side any additional tax due on a lifetime transfer that arises as a result of your mother's death should be reduced, as her nil rate band will have increased.
Here is a link to a worked example to illustrate this last point.
I hope that helps