[Ruling on One Who Vows to Fast an Unspecified Month]

Answer—and Allah is the Granter of success: He is not obligated to observe consecutiveness; the default is that one’s liability is free of the obligation to join fast-days consecutively.
If it be said: The unqualified word “month” (shahr) denotes consecutive days,
We say: In this vow the man intended by “month” fasting thirty days; he paid no heed to whether they were consecutive or not. His intention attached to fasting that number of days, and he did not intend consecutiveness in his vow.
Moreover, even if the word “month” in the language commonly denotes consecutive days, in vows what is determinative is the vower’s intention, not the language.
Yes: what we have mentioned may be given some support by Allah’s saying: “then fasting two consecutive months” [al-Nisāʾ:91]. The apparent restriction to consecutiveness here indicates that, when left unqualified, the wording is open to either: consecutiveness or non-consecutiveness. In that case, the default is that one’s liability is free of the added obligation of consecutiveness.
There is also a report mentioned in the books of legal theory: that a woman vowed to fast a month (or two months), then died before fulfilling that. Her daughter sought a ruling from the Messenger of Allah—May Allah bless him and his family and grant them peace—asking whether she could fast a day or two on behalf of her mother.
The Messenger of Allah—May Allah bless him and his family and grant them peace—said: “What do you think: if a debt were upon your mother and you paid a dirham or two toward it, would that benefit her? …” and so forth, as narrated.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1