Working permanently in the EU for my UK employer

I am an EU citizen living and working in London for a UK employer. I am able to do my job fully remotely.

My partner got a great job in Germany and we are moving in the summer.

I want to convince my employer to let me work permanently from the EU. It’s a small company and there is no HR/Legal advisor and my employer has never done this before so I need to guide them on what to do and what costs are associated as i may need to cover these myself

In a chronological order, what steps do I need to take? Any before I move, or only after? I want to better understand the timeline of what’s needed from me and then and by when. Let’s say we move on the 1.6.2025.

Danke!