The answer to this — and to other mobility questions that arise time and time again — can be found in this very helpful and concise article by Abbiss Cadres.
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Do we need to translate the contract into the local language? This depends on the location but in some countries any contractual documentation will be void unless it is in the local language. Where this is the case, if the employee or employer still want an English version (for example, as a reference source or to assist a centralised HR unit in managing the employee relationship), the usual course would be to prepare any document containing contractual terms in dual language format in two columns, one in English, the other in the local language.