Hi, welcome to UKY and good luck on your upcoming visa application!
For most UK/US couples, getting a mortgage is something that's probably more of a longterm goal after immigrating. Unfortunately, even if the US expat has absolutely amazing US credit, it will mean nothing in the UK. For all intents and purposes, the US expat will need to build up UK credit from scratch and upon arrival, will be treated as having no UK credit history.
In addition, sometimes probationary immigration status is a hurdle to overcome as well - until your partner gets permanent residence after 5 years, even with a built up UK credit score, a reasonable mortgage might not be on offer until both parties have good UK credit and settled status.
There have been a few instances where people were able to get mortgages soon after arriving in the UK, but generally only under specific circumstances. For example: Being able to put down more than a 50% deposit, having a very high salary/significant financial assets, or where the mortgage was done only in the name of the UK citizen partner and the UK citizen had enough financial clout to qualify for the mortgage solo.
As soon as your partner arrives in the UK, we recommend to try and get a starter credit card to begin building up credit history. When opening a bank account, see if s/he can get a modest overdraft. Some banks might offer "new to the UK" packages to help start building credit, and will allow a small overdraft and low-limit credit card when opening an account.
If s/he cannot get approved for a pay monthly phone plan in the beginning, try doing pay as you go for a few months and then try upgrading to pay monthly. Also, your partner can contact the credit agencies to explain that s/he has a valid visa to be living in the UK but is not a citizen [yet] and so is not included on the electoral roll [yet].
These are probably some of the best ways to try and jumpstart building UK credit as a newly arrived expat. It is frustrating that if you have wonderful US credit, it means nothing in the UK.
But all this is in the future - focus on the visa first.
And feel free to ask any questions!