Common, that's not exactly what happened - she was offered an internal transfer. Every company I have ever worked at had a simple rule: you will not earn less. On the flip side do I also know so large Swiss banks having the rule that you cannot be offered more if you transfer internally... (which is the very reason why so many switch from one bank to the other and back...)
I think it's a fair assumption that if a line manager in your company knows your salary, offers you a position and nothing else is said you simply continue to get your salary as is. For internal transfers do you typically not even sign a new contract, but get a one-pager saying PapaGoose will from date x on change to the position of y working in department z.
Bottom line: OP, don't get a lawyer yet. You are morally right, but going to court is an absolute last resort. I'd suggest to try a couple of other things first and only if nothing helps get legal help.
You sound like you are at the point that the bridge with the new guy is burned(?). If yes, escalate it:
1. Talk to your current line manager and discuss the case openly with him. Maybe he wants you back? No need to be ashamed of quitting on him before - openly tell him why you wanted the other position and that you now want your old one back as he might have the less appealing job but clearly is the better manager... trust me, this works with a lot of people...
2. Talk to the new guys superior. Even if you decided to not work for the new guy anymore, he should know. I am heading a department and I really would want to know if my team leaders cock stuff up like this...
3. Make a formal complaint to HR. Not the person who probably sit there with you and the new guy discussing the salary, but whoever the highest HR manager is you can get a hold of. In any decent company did your future ex boss break an entire bunch of policies (that's not necessarily Swiss law, but internal company policies)... no company HR wants managers to poach each others employees to only alienate them with ridiculous behavior afterwards.
4. If absolutely nothing else worked - go one level higher and write to your department head or depending the size of the company CEO directly and express how you did a good job in the past, identify yourself with the company and were super motivated to get an internal transfer - only to be forced to leave if no solution is found.
Bottom line: I do not agree with some of the others here that it's your fault that you did not sign something - I think this is standard practice in large companies. Make a fuzz about it and think your options through:
- go back to the old job? Yes, it has been communicated that you'd change... but do they have a replacement yet? I know it makes you feel a bit embarrassed to your peers and old boss, but honestly: the other manager screwed it up and well... shit happens.
- it's certainly not a good to start with the new boss, but well: maybe if he gets a bit of a dressing down from the top HR on how he behaved things can be fixed. I know first impressions are important, but well - all those alleged budget reasons are things that can be adapted and fixed a level higher.
- other jobs availabe in your company?
Only if nothing of this works out I'd leave. I would not sign a contract with a lower salary: It will affect you worse than leaving - if you earn less will you for example also get less unemployment benefits if you decide to leave later.