She should chase up the PC application by calling 0800 99 1234
They will send out an MI12 form as part of the PC application, which gets filled out by the claimant then sent to the mortgage lender before going back the the DWP. This in itself can take 4 weeks.
As the person who is named on the mortgage will be the partner on the Pension Credit claim, then that will not be a problem.
If awarded PC, they will get up to £69.81 per week towards the mortgage interest (paid every 4 weeks to the lender)
If this is not the original mortgage, ie if they have remortgaged, then the DWP will ask for more info.
Also, if they haven't done already, they should inform the mortgage company about the situation.
Hope this helps.