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Certainly, you do not fulfill your obligation if you send to a poor person in Bnei Brak on the 15th, as the time of Purim has already passed for him.
If you send Matanot L’Evyonim on the 14th while you are a Yerushalmi: If we follow the status of the recipient, you would fulfill the obligation because he received it during his time of Purim. However, Maran the Chazon Ish (see Teshuvot VeHanhagot 1:404) holds that since you yourself are not obligated on that day, you do not fulfill the obligation.
Regarding Mishloach Manot, according to the reasoning of the Manot Halevi, the obligation must specifically be performed on one’s own day of obligation. Therefore, while there are sides to be lenient regarding Matanot L’Evyonim, regarding Mishloach Manot one must be stringent and ensure they are given on your own day of obligation (the 15th).