The particle へ in 山へ面している

Question

tl;dr: Should へ be replaced with に here?

I was reading Imabi and found the following example:

小屋は山へ面している。

As far as I know, へ is used with motion verbs especially when transition from one (current) location to the destination (marked by へ) occurs:

A particle that indicates the direction toward which some directional movement or action proceeds. (A Dictionary of Basic Japanese Grammar)

Why do the author of Imabi use this particle in this particular situation if the word [面]{めん}する means to front/to face smth?

I know another particle that can be translated as "towards" — を, but according to Imabi it requires an action verb, what (in my opinion) the [面]{めん}する is not.

Another particle which can mark direction is に, which can replace へ in most cases. に can also mark indirect objects, so I believe it is the best candidate to replace へ.

FYI: This example is Ex. 18 in 第36課: ～ている

Answer 1

BCCWJ has 1100 instances of に面し/に面す but no instances of へ面し/へ面す, so you should always use に. That said, we can still find some examples of ～へ面していて on Google, and I personally feel they are not awfully bad. Meaning-wise, I see no difference.