Moving some of my auto-entrepreneur business to the UK?

At the moment I have a small business in France which I have as an auto-entrepreneur. The overheads are high and the profit is low. It does, however, take up all of my waking hours. At the moment my auto-entrepreneur activities allow me to produce the product, distribute and do the admin etc. My customers are all in France (well 95% of them). I am currently resident in France.

My son (UK resident) is going to start to do something similar in the UK under the auspices of a UK Limited Company. He is considering taking over my business so that all the admin and accounts and web admin and production work are done from the UK. He will in effect have two ‘sister’ lines of production going on. He has the time, and skill for this.

My plan is to amend my auto-entrepreneur registration to that only of admin and distribution and then act almost entirely as a distributor (not seller) as accounts would be dealt with from the UK. Literally delivering. Plus a small amount of Admin to help him out. All payments from French clients would be made via electronic payment into a UK bank account.

Do you think that this would work? I would not be a director of the UK Limited Company and would simply invoice them for my time delivering and doing any admin. Whilst I would be a sort of representative in France I would not be able to bind the UK Company - they would quote and accept work. I realise that as an auto-entrepreneur I would need to be able to invoice for my time to more than one company, would I be able to invoice my husband for admin for his auto-entrepreneur?