Is this your first true spider?
How soon did you wait to offer the spider food after you moved them into the new home?
How do you know the spider is in pre-molt?
No one is here to judge you fyi, just answer those honestly and I can give you some good help.
Spiders can be in pre-molt anywhere from 1 day to many many weeks. Given how juvenile this spider is, I'd say it would be in pre-molt about a day or 2 at most. Small spiders don't really have heavy pre-molts, that is usually tarantulas and larger spiders.