Hi Paul
Everything you have found seems to be correct, also the correct parish, but their moving in record is missing or they changed their minds and went elsewhere, anyway.....
........not easy this one. I had to start backwards. Here is Per Larsson's last entry before his death in 1912:
Västra Sallerup (Eslöv) AIIa:14 (1908-1917) Bild 240 / sid 14 (AID: v266965.b240.s14, NAD: SE/LLA/13478)
I think you should be able to trace them from here. You will notice his wife's death date recorded too. Her death entry should give you a page in the household book.
I do know they lived in Eslöfs Köping in 1890 in Västra Sallerup/Eslöv.
Ian