There is something you might tell her. It doesn't help with the immediate problem, but it might help her put things into perspective.
In many companies, recently hired IT staff earn more than longer-serving, theoretically more senior staff. That's because right now there is a shortage of IT staff, and changing jobs is an excellent opportunity to negotiate. "10% more or I won't start here" is much more credible than "10% more or I quit." Most people don't quit lightly, even if the job market where they live makes it relatively risk-free.
The lesson for Alice: In a few months she will either be looking for a job or negotiating about staying on. She should inform herself what Fachinformatiker earn in the region and negotiate accordingly. Can she wait that long?
Also consider:
- Alice will soon end her apprenticeship. Why is she getting the same amount as someone in the first year, anyway? It is common to increase the Ausbildingsvergütung year by year. Somebody (and that might be you or the Betriebsrat if you have one) could raise that issue, without direct reference to Alice.
- Alice may qualify for BaFögBafög. Has she looked into that? In extreme cases, she might qualify for supplemental welfare (Aufstocker).
- Regarding fairness and making ends meet, the housing market is overheated in many German cities right now. Someone who has rented her flat last year and not two or three years before might face substantially higher rent, at no fault of her own. This other trainee might be in an even more desperate situation than she.