Living in Greece but working for UK company

Hi everyone,

My partner and I have just moved to Greece and are looking for help on how to set ourselves up in terms of tax, company, self employed, etc But it is different for each of us but we both have AFM / tax numbers.

1) Me: We live in Greece, but I am working for a UK based company and my role is based in the UK. My manager has simply allowed me to work from home which now happens to be in Greece. The work I do is all for the UK and no services or products or anything is connected to Greece.
My employer pays me into my UK bank account and deducts the tax and National Insurance (Social security/health). From their point of view nothing has changed and HR won't do anything differently.
So if I am living in Greece I need to pay Greek tax. But how do I do this without paying twice? My employer won't fill out any forms so it needs to be something I can do.
Is it possible to pay UK taxes and GR taxes and then claim back from UK once I've proved that I've paid taxes in GR too?

2) Partner: My partner is going to be working as a photographer. The money that he will make will not be too much for the first few years. He will be making about 15000 EUR per year and about 10000 EUR profit.
Now, is there such a thing as a freelancer in Greece? What tax does he need to pay?
What about health insurance? I've heard this is about 500 EUR every 2 months which is a lot when he makes so little.
Or should he setup a business?
Could he set up a UK company and pay himself a small salary every month?

Thanks for all your help