How toyour friend can possibly get what your friendshe wants
AlsoFinally, as already suggested by other answers, I would start with smaller levers than quitting such as refusing extra responsibilities.
But mostMost importantly, your friend should think strongly about whether a salary increase is actually what she wants, for several reasons:
The academic apparatus is not geared to rewarding people with money. In most fields, people who care about money leave academia, and academia doesn’t need people who are in it for the money. (This is not supposed to say your friend is obsessed with money or similar.) The rewards of good work in academia are rather that you get to stay in academia, get more funds (not for salary), etc., in particular before the professor stage. I would therefore suggest that your friend considers seeking alternative “rewards” such as a permanent position, personnel to help her advance her own science, etc. (Paradoxically, funds for this may be more easily available.) This is particular important as:
The main risk I see for your friend is this: If she wants to pursue a classical academic career, one of the main thing she needs to show is her own research output. Taking over the group leader’s duties can give relevant experience in teaching, supervising, etc. and those are not worthlesshave value in future applications, but they can only compensate so much for a lack of research. (Mind that this is a vague guess: Your friend may actually get a lot of career-relevant research under her name, in which case she may be already in for a long-term reward, as she has well rounded group-leader experience.)
A salary increase does not address this and is worth very little if your friend has to leave academia – probably around the time when the actual benefits of the salary increase would start kickingkick in, because:
The actual short-term increases to salary may be rather low because the German public salary system has two axes, one for responsibility/qualification and one for job experience. If you friend progresses on the first axis, she will probably take a step back on the other axis. She cannot lose salary (by law), but the real benefits may only manifest as she steps up the experience ladder faster and with more benefits. Details depend on her current experience. This contributes to why this is usually done only in latter career stages (for postdocs and similar).
Your friend has to be the judge whether to seek her group leader’s support for this. They may support this, in particularly if the goal may not be actually leaving the group is not the actual goal – but they may also equate it to a threat to quit or feel betrayed.