NavList:

Sorry for not getting back to you. From my perspective, once the "nautical astronomy" was resolved (in other words, the latitude), the scenario was done. But of course, I do understand your curiosity!

I don't know if that's a church or maybe a Wake Island "Christians' Club", or (less likely, I think) it may be a misplaced photo. The latitude is consistent, and the image was listed by the photographer as "Wake Island". In addition, there's a substantial antenna structure visible in the original photo either attached to that building or behind it, which is consistent with facilities on Wake. 

The catch with identifying this building is that there is no local population and no tourism industry on Wake Island. Local photos are few in number. It was a "desert island" with scarcely any role in history before about 1930, and after that, excluding brief Pan Am Clipper service (thanks to Juan Trippe), its history is almost entirely military. The consequence of this for us is that photography is limited. In the aerial/satellite views, one thing for certain is that there are many small buildings oriented about the right way that might be this cross-topped building. I poked around after you first asked and couldn't find any certain hit.

My opinion: I am fairly confident that this building is on Wake Island. The latitude by celestial details matches Wake. The photo was posted as "at Wake Island". I'm not confident that it would even be listed as a church. We do know that there are many sincere Christians in the US military as well as among contractors connected with military operations on Wake Island. This may be now (or may have been a few years ago) a "temporary" place of worship.

Frank Reed