Write to someone
Incorrect : She writes me every week.
Correct : She writes to me every week.
Note: “write' cannot be used as a transitive verb with a single object referring to a person. But you can say:
He writes two letters every day.
Here the object refers to things. Again, when there are two objects after the verb "write”, you can omit the preposition. For example:
She writes me two letters a week.
But when the direct object comes first, the preposition is again necessary. For example:
He writes two letters to me every week.