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If you have a look at the following two Wikipedia articles:
http://en.wikipedia.org/wiki/Old_High_German
http://en.wikipedia.org/wiki/Old_English_language
you will see that the two languages probably started to diverge in earnest around 500 AD.

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But it also becomes clear that only very few written material is available today from that period, and because of this there are considerable uncertainties involved.

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Put on top of that a lot of people wandering all over Europe in those centuries, and your question probably becomes quite impossible to answer...