Pending loop when trying to move rings using the insider app on XSX

You could try uninstalling the insider app and reinstalling it, sometimes there can be issues server side when you move rings

I never got an invite but just kept checking the Insider app until the option to move to the Alpha Ring appeared.

If your friend is in the Xbox Insider Program, it might be that the Guide re-arrangement feature is currently in testing for the Alpha and Alpha Skip-Ahead rings. He could start the Xbox Insider App and check which ring he is enrolled in.

If he's eligible, he might have the chance to move up to an Alpha ring, but also at the risk of new stuff not working. So he should really consider if it's worth moving up to a less stable ring.

When that new feature is being released to lower rings or the general public depends on how many issues the Alpha Testers find with the feature.

Only if it's considered to run stable, it'll be released to lower rings or for general availability.

I never got an invite but just kept checking the Insider app until the option to move to the Alpha Ring appeared.

"Only" checking the Insider App is not enough. If there are surveys and quests you can do, do them and answer the survey questions.

Also, if a Beta-Feature is particularly helpful or does not work as you would like it to work, file feedback. Hold the Xbox button on the controller and use the send feedback button, when you encountered a problem.

The more feedback and surveys you file the more "active" you are regarded as a Insider, and the higher the chance of getting an invite to the Alpha ring.

Once you have downloaded the Xbox Insider Hub app onto your console select the option on the left of Insider Content and from here you can enrol your console in the program. Please be aware your console will probably start in ring 4 and only get updates
when they are nearly ready for general release. The status of pending will change once you enrolment in the program is complete but this may take a while.