Import translations from a different Gettext file

I have a C software translated through Gexttext and already-translated .po files.

I have the HTML documentation of that software, similarly-translated.

Both translations share some strings, namely the names of the settings, options and controls. I would like to init the documentation .po with the software .po. Said otherwise, for each msgid of the doc .po matching a msgid of the app .po, I would like to import the msgstr.

So far, I tried msgcat and msgmerge, but probably because the Gettext metadata don't match, they don't merge anything.

I have used Poedit too, with some success (loading the app .po as if it was a .pot), but I would like a scriptable option.