Consent might not be necessary or might not be possible, depending on the situation. You need a legal basis for processing of data, one possible (but the worst

Consent might not be necessary or might not be possible, depending on the situation. You need a legal basis for processing of data, one possible (but the worst possible) is consent. A popular better one is "fulfilment of a contract". All that is largely (but not completely) independent from how and where the data processing is done. You usually do not need consent to have data processed by a third party or abroad, if you have a legal basis for processing said data. You just need to keep your customer informed. Exceptions to all this apply for special kinds of data (minors, medical, biometric,...) and invasive processing (AI decisions, scoring). In those cases you might need special consent or you might not be able to export the data at all, even with consent.