Do You Move In to or Move Into?

Here’s a question a reader posed. It is worth some thought:

A person is moving from one apartment to another. Would you say she is moving into the new apartment or moving in to it?

I vote for the first option. She is moving all her belongings inside the new digs; therefore, she is moving into it.

If you say she is moving in to that apartment, you are thinking of the verb as “moving in.” But that “in” is extraneous. She’s moving. You could save space and trees (OK, a tiny tree) by simply stating she is moving to her new apartment.

Feel free to disagree.