Is it obligatory to re-fast the two consecutive months if the last days of the fasting coincide with the last days of Eid al-Adha?

Among the conditions for the validity of a vow is verbalization, not mere intention. If a vow to fast for two consecutive months is valid, then one must fast them consecutively. If Eid or the days of Tashreeq intervene, the continuity is not broken; what was missed of the fasting days is made up, and one builds upon what preceded. However, if the vow was to fast for an absolute month, then continuity is required. If one breaks it without an excuse, one must restart. If one breaks it due to an excuse, one is given the choice between restarting the fast or building upon what has passed, along with an expiation for the loss of continuity.