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Pensions are made by 2 elements:
A) Basic plan (State plan)
B) Additional funds (pension funds in some countries, pension by compensation)

The right to pension is calculated according to the social security paiements throughout your work duration.

When you work in the European Union and you pay social security, the Communautary Law applies and you get your right to the basic pension plan A) continiously wherever you work. For additional pension funds B), the equivalent is different in the coutries. In United Kingdom for example, it will be the Pension Fund (private contribution) and in France a Pension by Compensation. There is no automatic transfer with the State pension plan A).