Replacement to DR05-1510
Thank you for your patience during this busy season. The 82-108 does have the outer mounting holes. You can see them more clearly in the first dimensional diagram we show on its store page, which I will also post below for your convenience.
The metal posts do not connect to the pull, no. You have it backwards; the posts actually go inside the door. The pull handle actually doesn't mount to the 82-108 in any way. It mounts to a tertiary piece, which itself mounts to the 82-108.
I think you should look at our 82-080 for a better idea of how this handle set is supposed to look. The interior portion of the set is comprised of four pieces: the pull, the pull base, the 82-108 mounting plate, and the 82-240 thumb lever.
Looking at your photo here, you're showing the pull and pull base. I don't see the mounting plate. The pull screws to the pull base, and the pull base sort of "plugs" into the 82-108. The screws that come in from the sides secure the whole thing.
That tertiary piece is unfortunately not sold separately. The 82-108 is the only component of the 82-080 kit that is available by itself. Everything else is only included with the kit. I've never seen this piece sold separately and I am not sure that it will be possible to get it. I hate to say it, but if that's what's broken then you should strongly consider an overall replacement.
Even if those two pieces could work, it's important to understand that they change the design of these handles all the time. I've seen several instances where the 82-108 itself was too skinny or even too wide in some cases, and was therefore incompatible. It's designed only to work with the 82-080 in its current iteration. Over the years I've found it to be more reliable to just replace the whole handle.
I am sorry for the inconvenience.