Translation:My mother always sets her coffee here.
In this particular sentence though, what would be the difference between "set the coffee here" and "set the coffee down here"? (I guess I'm asking both about English and German, since I'm non-native speaker for both: it really feels like if you set the coffee somewhere you necessarily set it "down" somewhere)
In my mind, if you "put [something] down", the emphasis is on the the fact that the object left your hands. If you "set [something]", the emphasis is more on where you put it. In this case it's a habitual action giving import to the location, so "set" is appropriate. But you could also say "My mother was so shocked that she had to put her coffee down."
PS: This is all just based on my intuition as a native English speaker (US Midwest/Northeast).
Both "sets" and "puts" are correct. If "puts" is being marked incorrect, then report it. Complaining here won't accomplish anything.
Also, if you're mad about being marked wrong, post the entire sentence that was marked wrong. In many cases it's not the word that you think that caused you to be marked wrong.