Lasercutting - RGB colours from Illustrator appear in grey/blackwhite after export to Rayjet Manager

Hey there 🙂
I'm using Illustrator quite a while already to create the files for Lasercutting with Rayjet Manager (Lasercutter from Trotec) for my job. In my latest file I'm facing a problem which I never had before and couldn't find any solution yet. I hope to find some help here because this is my last chance. I'll be very thankful for any suggestions in short time.

A colleague of mine drew a design in ArchiCAD and sent it to me as a DXF file, which I opened in Illustrator and edited there. As I'm used to Illustrator, the settings like RGB colours, line thickness of 0.01mm & co are familiar to me and all set correctly. But nevertheless, when I 'print' the file to Rayjet Manager, there the red/black/green lines suddenly will appear in grey. I attached some partly screenshots to make clear what is my problem.
I already called Trotec/Rayjet Manager Support and they are sure, the problem is not there and I can also say that, because when I open a whole new document and quickly draw three circles - one in red, one in green, one in black - and then export that to Rayjet Manager, it is displayed correctly. When i copy part of the problematic design to that new document with the circles and export that again, it will appear in all grey again. So I'm pretty sure, the problem is with the imported data from my colleague. All lines are paths and after editing the design, I saved it as an .ai file.

Does anybody have any idea what could be the problem? Is there any setting in the background which is important? We already spent so much time in creating that design and finding a solution and want to produce as soon as possible.
Thank you sooooo much!