The solution is to add the below to LocalSettings.php
on the source wiki:
$wgUploadBaseUrl=$wgServer;
This adds the proper scr= attribute to the <img> tag which means that
the transcluded article also pulls through the image.
Make sure you also set the following on the local wiki:
$wgAllowExternalImages = true;
$wgEnableScaryTranscluding = true;
So no $wgSharedUploadXXX configuration or NFS configuration is
necessary at all.
Allowing all external images is rather overkill. If you just want
images from one other wiki, shareduploads seems like your best bet.
Since it's an internal wiki you're talking about, turning on external
images is ok, but it isn't generally a good idea on publicly editable
wikis.