Q:

Is it correct to say "someone's heart is with us"?

Is it correct to say "someone's heart is with us"?
I'm trying to translate a piece of text to English and I really don't know whether that is correct or not. The source text is saying that someone is wishing to be with us and do something together, but he didn't succeed. So we are questioning whether he was truly intended to be with us or not? That's the part I need to know if it is correct to say that phrase or not.
I have checked some dictionaries but didn't find the meaning I was looking for.

A:

It's not clear from your question whether the absent someone has declined to join the group for a social outing or has failed to turn up to support a cause for which the group was rallying. If the latter, then the metaphorical use of the word heart to indicate feeling or emotion is apt. The use of heart to indicate innermost feelings goes back to the origin of modern English. The OED finds written references almost one thousand years old.
Here's Abraham Lincoln talking about the struggle against slavery and for the maintenance of the union of the United States:

The human heart is with us —- God is with us.

The other side spoke in the same terms: Here's Jefferson Davis some fifteen years before he became the President of the Confederacy writing to a friend about another President of the United States supporting slavery:

As I have often told you, his heart is with us.

Here's a more modern usage: Vishay Prashad in his book The Darker Nations, quotes the Iranian poet Forough Farrokhzad in her poem "Someone Who Is Not Like Anyone" about the Mahdi, the redeemer prophet of some Islamic sects:

Someone is coming
  Someone is coming
  Someone who in his heart is with us

The usage is somewhat poetic and used for issues of deep concern or emotion. Closely related is the English idiom, "not to have one's heart in it," i.e., to do something one isn't really emotionally committed to. For example,

Joe is still attending classes, but it's clear his heart isn't in it.

In other words, Joe is still dragging himself to class but not because he's committed to his education.

