Something not quite right here folks. The op's profile says British

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| 2. If i choose the 2nd company, will there be any complications arising in doing the above said (as the first employer may already have started the paper work with the Cantons)? | |
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Why would they do anything if you are British?
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| Not knowing your present work visa status I have a third question: Do you already have a work permit for the canton that you're presently in and will it allow you to relocate to a different canton for both living and working..? | |
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Doesn't need one. British

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| Yes, I currently have a B permit, it allows me to work for any employer as per my present Canton's words.
Whereever I relocate the new employer will just have to inform their Canton about my employment. This is what the Canton officials said to me. | |
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No such obligation exists for British citizens.
Anyway, back to the orogional question for this British op it appears that what was signed was not an employment contract but rather a letter accepting the position. These letters are always subject to contract therefore the obligation is not really there.