Unmarried Partner's Visa: ILR is in previous passport

I'm going to apply for unmarried partner's visa in May.
My partner is not a British citizen, but lived here for 25 years and has his ILR. He got his new passport recently, and haven't transfer his ILR to the new one.

Is it better that he transfer his ILR to his new passport before I apply for unmarried partner's visa? or it doesn't matter.

Do you know which number to call to make sure that they accept ILR in previous passport?

It really doesn't matter - he can just carry both passports.

The IND website is even slower than usual at the moment, so I can't double-check that the page is the same, but a couple of weeks ago, the bottom of this page on the IND website said the following:
"...However you should be aware that you are able to travel with a new, valid passport without having your leave transferred provided that you carry with it either your old passport with your endorsement of leave, or the letter on which your leave was granted."