he must petition at the centre of his main interest for the last 6 months.
so at the 3 month stage you are half way period.
if he has brought all of his belongings south of the border then later this month North England will be the centre.
If however he still has the majority of his belongings still in Scotland but just renting due to job then his COMI would still be Scotland.
He may have to produce bank or shop receipts showing home. ring the clerk to the local court and ask for their guidance.
I know that Scottish systems for declaring BR are slightly different. The courts are clamping down on bankruptcy tourist so they are quite hot on making certain that the COMI is correct
I was in a similar situation having moved to a different area a couple of months before I was declaring BR. I would recommend emailing the BR Clerk (their details are on the above link) explaining the circumstances and asking if you can apply for BR in their current location i.e. the North of England. The Scottish BR process is different to that of England/Wales and, from what I have read, not as straight forward.
The court fee is £100 in Scotland vs £600 in England. However it is not straightforward to petition in scotland.
Options;
1. You need to have a low income and be on specific benefits
2. You need to have the "approval" of one of your creditors whom you owe £1500 to . This is where the creditor signs the opetition agreeing that they don;t mind if you petition.
3. you need to have court action started by a creditor and the document served by the High Sherrif.
If your partner can qualify for any of the above then Scotland is cheaper. If not then hang on a little until they are clearly now resident in England ( 4 - 6 months ) and they can petition here.