I'll assume that your Gran died in Scotland and that consequently, as your post implies, Scottish law applies.
Quote:
"If there is a will
You should go to the sheriff clerk's office and take with you:
* The will.
* Personal details of the dead person and his or her family.
* A full list of the estate and its value as it stood at the date of the death including any interest, dividends or bonuses to be added to any bank accounts, stocks and shares or insurance policies.
* The certificate of death.
The sheriff clerk will complete the necessary forms and if no further enquiries are necessary will issue confirmation within a few days."
That quote is taken from this really helpful (government) website which contains a great deal of information which might be of use to your mother:
http://www.scotland.gov.uk/Publications/2003/0 8/17011/21437
Chris