The answer to your question would depend on whether your boyfriend experiences the migraine headache during or immediately after drinking alcoholic beverages. If it occurs at a much later time, a relation would be unlikely.
However, one headache that is very common as a result of drinking alcohol is a "hangover".
In any case, you should try to talk to your boyfriend to stop, or at least minimize, his alcohol drinking because of so many other probable and definite bad health effects.
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