Is it permissible to drop a letter in the mailbox on the way to synagogue just before Shabbat? Since it is almost guaranteed that the postman will collect the mail from the mailbox and begin the delivery process at some point during Shabbat, would this be forbidden?
In truth, Halacha permits leaving a letter in a mailbox just prior to the onset of Shabbat, despite the likelihood of the delivery process beginning on Shabbat. For one thing, sending letters via regular mail entails a fixed cost of postage; the mail carrier does not get paid any more if he delivers the mail the next day. Hence, we do not consider the postman to be acting as the sender's direct Shalia'h (messenger), and thus no prohibition is involved. Furthermore, in this case one does not hand the letter directly to the postman, but rather places it in a box, and this is yet another reason why we need not view the carrier as working directly at the sender's behest.
A more complex issue relates to express mail sent specifically with a request for Saturday delivery. Hacham Bension Abba Shaul (Israel, 1923-1998), in his work Or Le'sion (vol. 2, p. 152), forbids sending express mail for Saturday delivery, even if one sends it as early as Wednesday. Nevertheless, Rav Shemuel Pinhasi (contemporary), in his work Daber Davar (1:16), writes that under extenuating circumstances there is room for leniency in this regard. Firstly, the person delivering the package invariably carries with him many other packages, as well, and by adding an additional item one does not actually cause him to perform activity forbidden for Jews on Shabbat. Secondly, when one brings the package for delivery, he does not hand it directly to the person who will deliver it to its destination on Shabbat. This is therefore a case of "Amira Le'amira" – instructing a gentile to instruct another gentile to perform Melacha (activity forbidden for Jews on Shabbat) – which Halacha treats more leniently. And if one sends the package with the governmental postal agency, then we certainly do not look upon the delivery personnel as messengers acting on the sender's behalf. Hence, in situations of dire necessity, one should consult with his Rabbi to determine if whether he may send a parcel for delivery on Shabbat.
If a person in the U.S. wishes to send a telegram or some other form of correspondence to somebody in Israel, he must not do so on Friday afternoon, once Shabbat has already begun in Israel. Since it is likely that a Jew will be processing the correspondence from the U.S., one may not initiate such correspondence once Shabbat has begun in Israel, as he would then be causing other Jews to violate Shabbat. (Rav Pinhasi codifies this ruling on p. 70; listen to audio recording for precise citation.)
It is permissible to leave a letter in one's personal mailbox outside his home before Shabbat, so that the postman will take it for delivery on Shabbat morning. There is no concern of "Mar'it Ayin," namely, that onlookers will suspect the person of violating Shabbat.
Summary: It is permissible to put a letter in a mailbox just prior to Shabbat, or to leave a letter for the postman in the mailbox outside one's home before Shabbat. One should not send packages for Saturday delivery; in situations of great necessity, one should consult a Rabbi for guidance, as in some cases there is room for leniency.
