Thanks for the answers.
The Chinese maker sent me the file types they can manage:
PDF
PSD
CDR
AI
JPG (I don't know about this one, they say they don't manage bitmaps...)
Unfortunately I had no luck in making Illustrator to work on my Mac and that is why I found Affinity (I've been using it for 2 days now, but I really like it).
So, in theory they should be able to use a PSD, but they said they can't. Something lost in translation.
However, they told me we can try with PDF to see if it works. That would be the best because the PSD is about 80Mb and the PDF is 25Kb.
Just sent them a PDF, finger crossed.
M