From another comment I understand they also have a UK presence. Are you a true-blue employee or a contractor who takes care of their own taxes and affairs, and just issues monthly invoices? If you are an actual employee (in the legal sense), are you employed by the UK or US company, or something else? Do they have to have an address there, or a foreign subsidiary? Presumably there's no German legal entity, so how have they registered there to pay tax?
This is something I'm prospectively interested in doing for my own business, but I'm not sure how I'd make it work from a tax point of view.