The correct answer is "A. have lived".

The sentence is in the past tense and refers to a completed action that happened in the past and has a connection to the present. The use of "before moving here" indicates that the action was completed in the past. The present perfect tense "have lived" is used to describe an action that began in the past and continues up to the present.

Therefore, the correct sentence is "They have lived in Boston for ten years before moving here."

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