Ah, I see, from this point of view it does make sense (and thanks for the explanation, didn't know that yet!), but the action of putting a letter under a pillow doesn't really make sense to me (my first thought was that this might be some kind of Swedish superstition thing, like putting your teeth under the pillow for the tooth fairy?). There are surely more realistic sentences that could teach the same? Maybe putting the letter under a paper weight or something like that?
Would it be incorrect to say He left the letter under the pillow?
I know the literal translation would be laid, but as a native speaker my natural inclination for this situation would be to use left. The reason is left has a connotation of intentionally leaving something behind whereas put does not. It takes intent to put a letter beneath a pillow. It would be different if the letter were placed on a table, a situation that would not imply intent.
"Left" would mean to me that he put it there after his parents came in (see comment above) and then left it there when he went to school in the morning. Very careless. He surely didn't make his bed - being a teenage boy - so if his mother came in to tidy up for some insane reason she might find it. Point being ... I think "put" works here.
I didn't change the sentence, I just added another accepted answer. The reason I added it was that I think the Swedish sentence can mean that the letter was left intentionally under the pillow for someone else to find. I might prefer to express that situation in Swedish with lade rather than with lämnade. Anyway the point in lade is that the letter ends up in a horizontal position, so it doesn't correspond closely to English to begin with.
I'll take a shot at that one, because I get "Lay" and "Lie" mixed up myself sometimes. The Swedish sentence is is past tense of the word meaning to put or place. The word you want to correctly use is "Lay" meaning "to put." lay... laid... has/have/had laid
To lie, on the other hand, means to recline. lie... lay... has/have/had lain
The problem is that the past tense of "lie" is the same as the present tense of "lay." In this sentence you need the past tense of "lay" which is "laid."
[And then there is to lie... meaning to tell a falsehood. lie... lied... has/have/had lied.]