Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
The recipient of a gift or an inheritance does not pay tax on it personally in the UK except in certain circumstances where the deceased estate cannot pay it. See here for more information. Any income produced by the investing of her inheritance will be taxable in the UK on your sister but not the inheritance itself.
A UK domiciled individual's estate is liable to UK Inheritance Tax unless they have effectively lost their UK domicile. I think it's fair to say that your Mother has lost her UK domicile and acquired an Australian domicile. A non-UK domiciled individual will only pay UK IHT on assets based in the UK. See section 5 here for information on domicile. Domicile and residence are not the same.
I hope this helps but let me know if you have any further questions.
I'm just following up to find out if my answer helped or if you have any further questions.