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I work as a contractor for a major company in Western Europe, since September. By contractor, I mean that I am employed by a company, which sells my time to a client (the major company). I am not bound to my client in any legal way, my employer is covered if I leave, so no legal issue here. Since I am on probationary period, I have to give my resignation letter to my employer with a two weeks notice and that's it.
Before signing my work contract, I warned my employer that I had applied to a job that was my dream job (and the very rare kind - only one position opened in my country this year), and I might leave very soon if I was taken. I also warned them that I had reasons to believe I would be shortlisted. The recruiting process took forever, but finally I know they chose me. I will begin to work on mid-January.
Here are my issues: my employer did not tell my client I had that job application waiting. And my client will have a peak in activity in January. They have been actively training me in prevision of it. My client also tends to hire its contractor after a while and I was likely to be hired in a year or so. My client is the biggest company in my region and in the field I am interested in and I very much like to keep a good reputation with them. My dream job will last 4 year at most and I would like to be able to come back to my client after those 4 years. I have also a profile that may be hard to find, and replace me in two weeks is simply impossible. Also, the quickest they replace me, the quickest they will be able to begin the training.
So, I'd like to minimize the inconvenience for my client, and also mitigate the resentment the client's employers might feel, without burning bridges with my current employer. I believe I need to leave at least a month to my client to replace me, and I want my company to warn the client (or to let me warn them) as soon as possible. How can I achieve that?
Edit: As it is said in commment, this question does not address my question, mainly because I am not looking for the pros and cons of giving a huge notice, but also because it's highly US centric and the norms in my country are not fixed by custom but by the law. I believe the misunderstanding came from my question and it's subject being messy. So, I hope this update will clarify it. If not, I'll welcome any comment.
Edit 2 and 3: A bit more clarification.
Edit 4: I modified the question again, thanks to the input I received.