Correct spelling, explanation: this form is correct because in love are two separate words put together into a phrase meaning loving someone. Inlove is thus incorrect because this phrase doesn’t function as one word. In love is the only correct way to spell it.

Definition of in love:
phrase, to love someone; also: to like something very much
Oh, I’m in love with this dress, I have to buy it.
We were so much in love and spent every minute together.

Synonyms of be in love:
adore
be crazy about
fall in love
have a crush on

Incorrect spelling, explanation: this form is incorrect because in love is not spelled together. There are two separate words in it, so inlove is the wrong form. It should be in love, as in to be in love, so to be in a state of love.

Incorrect spelling