Dear Mr Ridings,
Thank you for this complex and interesting question.
The answer is this: Since last year, Germany, and the entire EU (except Denmark, Ireland and the UK) apply a common set of "conflict of law" rules. "Conflict of law" is the area of law which says which legal system applies in a cross-border situation.
In common English, EU Regulation 650/2012 provides that the entire inheritance of a person is governed by the law of his last habitual residence, regardless of where that might be located (even out of the EU). This means that Australian law applies.
In its turn, Australian law may accept its own application or not. However, Australian law does not have one common system of conflict of law rules. Instead, each Australian state has its own rules.
Therefore, it is essential for me to know the specific state where the person in question resides.
This holds the key to your question, which can have the following answers:
1. The state law accepts its application and provides that de facto partners inherit, in which case your mother takes everything;
2. The state law accepts its application but makes no provisions for de facto partners, in which case your mother takes nothing;
3. The state law does not accept its application and sends the matter back to German law (note that this is an intellectual exercise, nobody "says" anything, but it is what the German courts would say). German law does not provide in any way for de facto, unregistered, partners. Therefore, in this case your mother would also take nothing.
As I am outside of my HQ country, please answer with the state of location, but know that it might take a few days for my answer to come back, because my database of world laws and doctrine is available only at my HQ. If it happens that the question expires in the meantime, I offer two options:
1. Either accept my offer of premium service, which will allow me to get your e-mail and convey the answer by mail. I set it at the lower end of the price range; or
2. You can then ask another question, but I think that would be all in all more expensive.
With my best regards,
Dr I L Vlad