I say, and with God's success: This is a conditional vow, so she is required to fast for a month, and continuity is not obligatory if she did not stipulate it or intend it. She has the choice; if she wishes, she can spread them out, and if she wishes, she can fast consecutively; because fasting does not occur at night, it is therefore separated. What is inherently separate does not require continuity unless explicitly stated, so continuity is not required unless she intends that. See: Al-Hadiyah Al-Ala'iyah, pp. 185-186. And God knows best.