This sentence would be so much nicer with "to" in it. I guess this is US English but it sounds awful to me
If you used "to" and your answer was rejected, you might want to report it. Perhaps it could become an accepted alternative translation, since "to each other" would be fine in English.
UPDATE ----- "They wrote TO each other every week" is an accepted translation.
If you're doing the version of the sentence where you pick from the words provided, there's no 'to' to include.
Such is life with side translations. Use your mobile web browser and you caan write anything you want a nd maybe you even learn more.
Your comment makes me think that Duo (not a course team) populates the Word Bank and does it based on the main translation only. Is that correct?
Anyway, I changed the main translation, it is probably better and at least prevents these problems and discussions.
I did find some examples of "write each other" in English books, but that will be the reason to keep it accepted.