Is it permissible for me to fast on behalf of my mother who vowed to fast for a continuous month, but she is unable to fulfill it due to her suffering from high blood pressure and diabetes?

Whoever vows to fast for a consecutive month is obligated to fulfill it, due to the Prophet's (peace be upon him) saying: "Whoever vows to obey Allah, let him obey Him." If she is unable to maintain the consecution due to illness, she should break her fast on the days she cannot fast, then return to fasting until she completes the month. She also owes an expiation for an oath (kaffarat yameen) for breaking the consecution. This is the view of the Hanbalis and the old saying of Al-Shafi'i. However, if she is completely unable to fast, she must feed a poor person for each day, in addition to the expiation for an oath.