Is it "moved into" or "moved in to"?

At http://www.thefreedictionary.com/move+in , the Collins entry for 'move in' is:

move in [AHD says this is a phrasal verb] [so, a set expression]

vb (mainly adverb)

1. (also preposition) Also (when preposition) move into: to occupy or take possession of (a new residence, place of business, etc.) or help (someone) to do this

I'd prefer them to have

move in

vb (multi-word) (mainly used without an object)

1. (can also be used in this sense with an object) (the variant move into is usually preferred though when used with an object): to occupy or take possession of (a new residence, place of business, etc) or help (someone) to do this

They moved in last Thursday.

We're moving into a new flat next week.

Notice that 'move into' in We're moving into a new flat next week. has a different meaning from 'move' + 'into' in say The basilisk moved into the side-passage.

The verb is move. Into is a preposition complemented by my apartment. The construction contrasts with that found with a phrasal verb like give in, which requires to to be written separately in a sentence like I gave in to temptation, and had another beer.

If you mean "to switch residences," then make it two words because move in is a phrasal verb there. Prepositions in phrasal verbs become adverbs, and therefore, it is wrong to mix the adverb in in the verb move in with the preposition to. If you mean "to walk into the building," then make it one word because the verb there is move, and into tells us where you have moved (walked).

I'm sure you mean "to change residences," so make it like so.

I have moved in to my new apartment today.

Sources

1. http://www.macmillandictionary.com/us/dictionary/american/move-in

2. http://data.grammarbook.com/blog/definitions/into-vs-in-to/#comment-65310

3. http://www.quickanddirtytips.com/education/grammar/in-to-or-into?page=1 (reasoning)

"Into" is like "onto"… both necessarily dictate movement.

"I moved it onto the table" but "I put it on the table".

Going "into" (any space) describes the action of moving from another space to that one… thankfully!

Going "in to" (any space) describes the action of entering that space for a reason

"We moved into the apartment" or "we moved the table into the apartment" are fine, as is "we put the table in the apartment" but we cannot say "we moved/put ourselves in…"

Here, "we moved in to…" is a misnomer for "we went in to…"

"We moved in to…" might work in grammar, but idiom insists we use that form only in special circumstances, as when soldiers "moved in to clear the enemy out…". There, it should be clear that the area/place/space into which they moved is not clearly specified; their movement "in" and the enemy's "out" are conceptual.

Grammatically, that's the same as "we moved in to clean…" but idiomatically, we would normally only ever say "we went in to clean…" because in both cases, "…in to…" means "…in for the purpose of (cleaning)…".

Only if we were using sports-type terminology to compare our operation to a military mission might we say that we "…moved in to clean…"