Given that this involves Jews, the correct answer is that it is a machlokes. There are those who say that it can be done as long as it is sent to arrive on Purim. , and there are those who say that it cannot be done.
Another point is that sending to an organization that distributes on Purim is like making a shaliach to give it out for you. This is different from the case of mailing it to the poor person to arrive on Purim. However, the question still arises if one can have his shaliach deliver it on Purim for the poor person when it is no longer Purim for the original sender. Note that it would not matter if it is Purim for the shaliach or not as "shaliach adam kamoso".
There are those who say that the requirement of "on Purim" is established by the location of the recipient. This is not only based on the difference between Yerushalaim and elsewhere, but even for different time zones (such as Australia and the United States). This is cited in the name of the Eishel Avraham. The analogy is given to Mishloach Manos or Seudas Purim. Since the recipient is the one who will use it on (his) Purim, then it must be given on (his) Purim.
Matanos Levyonim - Laws and Parameters
If one is sending money to a poor person who keeps Purim on a
different day, for example in Jerusalem or a vastly different time
zone, the Purim is defined by the recipient, because you’re making his
day, and gladdening his Purim. (Eishel Avraham).
DO I FULFILL THE MITZVAH WITH MONEY GIVEN BEFORE PURIM?
If the poor person receives the money on Purim, one is yotzei (Be’er
Heiteiv 695:7; Aruch HaShulchan 694:2). Therefore, one can fulfill the
mitzvah by mailing a contribution if one is certain that the poor
person will receive it on Purim. If the poor person receives the money
before Purim, one is not yotzei (Magen Avraham 694:1).
However, there are those who say that this is not correct and it must be given to the recipient while it is Purim for the sender as well as for the recipient.
Sending Matanos La’evyonim and Mishloach Manos by Mail Before Purim
For example, one who sends matanos la’evyonim or mishloach manos by
mail in an instance where he knows that it will arrive on Purim and
therefore has kavana to fulfill his obligation via this method,
according to some poskim has not fulfilled his obligation since an
essential part of the mitzvah is the giving of the present which must
also be performed by the sender on Purim.
Note that this would imply that a shaliach can deliver it on Purim even if he was made a shaliach before Purim because shaliach adam kamoso.
עי’ ערוה”ש סי’ תרצ”ד סעי’ ב’. ועי’ ערוה”ש סי’ תרצ”ה סעי’ י”ז ולכאו’
סותר עצמו בסעי’ ט”ז, ואולי יש לחלק דאם שולח ע”י עכו”ם בדואר או המקבל
צריך לקח את החפץ ממשרד אחד כשיגיע לעירו אין שייך בזה שליח של אדם כמותו
However, most poskim disagree and maintain that one does indeed
fulfill his obligation, provided that the recipient received it on
. עי’ יד אהרן שמובא בבה”ט סי’ תרצ”ה סק”ז ובכה”ח ס”ק ט”ו. ועי’ שו”ת
חלקת יעקב בח”א, ועי’ פסקי תשובות
Some poskim want to extend this discussion to an instance where the
sender of the present lives in a regular city, and the recipient of
the gift lives in a walled city where Purim is celebrated a day later.
They maintain that in such a case where the present will arrive on
Purim in the walled city, one has fulfilled his requirement even
though the present was sent before Purim.
עי’ שו”ת ציץ הקודש סי’ נ”ו הו”ד בהמועדים בהלכה, ועי’ שו”ת דברי משה
ח”א סי’ ל”ח שהביא שבעל מנחת יצחק הסכים עמו דאם בן חוץ לארץ שלח ביום
י”ד לעניי ירושלים באופן שיגיע להם ביום ט”ו יצא ידי חובתו. ועי’ שו”ת אז
נדברו ח”ו סי’ פ
However, most poskim say that one cannot compare the two cases.
Although the recipient is receiving it on his Purim, however, since
the day on which he receives it is not Purim for the sender, he has
not fulfilled his obligation. Furthermore, even if the sender sends it
on his own Purim and the recipient receives it on his own Purim, he
would not fulfill his requirement according to these poskim since when
the item was received it was no longer Purim for the sender.
. עי’ שו”ת תשובות והנהגות ח”א סי’ ת”ד וח”ב סי’ שנ”ב מש”כ בשם החזו”א.
וכך שמעתי מהגר”י בעלסקי שליט”א. ועי’ שו”ת אז נדברו שם דלפי”ז יש להקפיד
במי ששולח ממדינה למדינה שיש הבדלי שעות. אכן שמעתי מהגר”י בעלסקי שליט”א
דאין מוכח כ”כ דבאופן כזו צריך להחמיר