Hello, it seems like the built-in weapon option doesn't work at all, nor the built-in mod or built-in wings :s
I did test this functionality before releasing it - my first guess would be some UI-friendliness difficulty. What exactly is the issue you are having, what step is giving you trouble? On my end built-in weapons routine looks like this:
1. Initialize layer with sprite and hull data
2. Place some weapon slots, switch their type to built-in
3. Switch to "Built-in Weapons" tab, weapon game data tab should become active automatically.
4. If desired, check necessary filter options, such as "Filter by last selected slot".
5. Select weapon entry from the tree, and then CTRL-Click on any weapon slot. The weapon should be installed in that slot and appear in the rightside tab list.
For hullmods and wings, you essentially select the relevant rightside tab and then right-click on hullmod/wing entries in respective game data tab to install them in either base hull or skin (skin file saving being non-functional at the moment).
There's drag-and-drop and workflow improvements already implemented for all these processes in dev version, but it's a fair bit of work away from update yet.
And, in case there is really some crash or bug going on, feel free to post steps to reproduce and logs - I'll look into it!