How did the tie end up in Anton's wardrobe in the movie 'The Night Visitor'

In the 1971 movie The Night Visitor, the sequence of events leading to Britt's murder is -

1. Salem breaks into his family farm and steals a tie belonging to his brother-in-law Anton
2. He leaves the farm with the tie at the same time when Anton is retiring to his room for sleeping
3. From the farm, Salem then breaks into (his girlfriend) Britt's home and kills her by strangling her with Anton's tie
4. Anton (who is a doctor) receives a call in the middle of the night from Britt's father to check-up on his daughter who is lying unconscious (actually dead)
5. Anton goes to Britt's house where she's already dead
6. After Anton leaves, police comes to Britt's house. Meanwhile Anton finds her sister-in-law (Emmie) dead in her room at the farm
7. The same inspector then arrives to Anton's place (the family farm) for investigating Emmie's murder
8. There the inspector found the same tie in Anton's wardrobe that Salem stole earlier the same night

This same tie becomes the reason for police to strongly link Anton with Britt's murder which also is clearly Salem's intention as well i.e. to frame Anton for Britt's murder and hence using Anton's tie to strangle her.

What I'm not able to figure out is, how did that tie end up in Anton's wardrobe? Did Salem put it back after murdering Britt (a possibility that doesn't seem to fit in the above sequence of events) or is it simply a plot hole?