Yes. Long coats are recessive, as is satin (which makes them shiny) and for that matter chocolate. Bred to a solid black shorthaired non-satin, you'd get solid black shorthaired non-satin babies het for LH, Satin and Chocolate.
This particular mouse, if she's full-grown, is actually not a bad specimen for a longhair - most longhair adult mice just look a bit scruffy rather than being really properly longcoated. That said, I've seen photos of longhair bucks that look like tailed hamsters!
Longhair is a bit of a pain being recessive actually - I'd like to breed it OUT of my colony (my foundation buck was a poor-quality scruffy longhair) but there's no chance, because any given mouse born here is almost certainly het for longhaired. And in the second generation I've had some LH crop up - some of which actually aren't bad, not just scruffies. I might try to breed a few proper longhairs, though that's a long-term project that isn't exactly compatible with 'breeding for snake food'... because I'd have to keep all the babies (of colours I liked) until they'd had a chance to really show what their adult coats were like.
