From a small booklet written by Nelson Ross in 1928, a guide on How to Write Telegrams Properly.
Handwriting in Telegrams — There is a classic joke of the telegraph business which may not be out of place here. A lady, filing a message with the counter clerk for transmission, first enclosed it in an envelope. When the clerk tore open the envelope to prepare the telegram for sending, she reached for it indignantly with the exclamation: “The idea! That is my personal telegram and I don’t want anyone else to see it.”
It must be remembered that a telegram is transmitted letter by letter. Telegraph operators, like post office employees, are expert in reading handwriting, but even so, words cannot be guessed at. If you write the word “opportunity” very clearly as far as “oppo” and the rest of the word is a mere scribble, it cannot be transmitted in that fashion. It must be “opportunity” or nothing. If you sign your name “John” followed by a series of hen tracks, neither can that be transmitted. You may have intended the word for “Johnson,” but you cannot reasonably expect the telegraph employee to be a mind reader as well as an operator.
How did telegrams hit moving targets? Like so:
Messages for Persons on Trains — A message addressed to a passenger on a train should show the name of the railroad, train number or name or time due, place where the message is to be delivered, and also the point for which the passenger is bound. If the train is run in 13 sections, the section should be specified if known. A sample address is: “John Smith, en route Los Angeles, Care Conductor, Southern Pacific, Train 103, El Paso, Texas.” Even though when the train stop at El Paso and John Smith is paged, he may be pacing the Platform for fresh air and exercise, the conductor will strive hard to effect delivery. If you expect to have occasion to telegraph a friend setting out on a journey, it is a good idea to get from him his Pullman berth and car number, so that you will be able to indicate this on your telegram. Telegraph clerks generally will be found to be courteous in aiding you to determine the progress of the train and station where it most likely can be intercepted.
And sending money was possible as well, using the HTTPS of its time:
The procedure is simple. A person wishing to send a sum of money by wire merely calls at the telegraph office, fills out an application blank, and pays the clerk the amount to be sent and the fee for its transmittal. The telegraph companies have a secret code which they use in directing their agent in the distant city to make payment to the person designated. The payee is notified to call at the office for a sum of money, or a check is sent to the payee, as may be directed. It is optional with the sender of the money order, whether the payee shall be required to identify himself absolutely or whether identification shall be waived. The Western Union Telegraph Company alone handles more than $250,000,000 annually in telegraphic money orders.
I wonder what sort of shenanigans telegraph hackers got up to trying to intercept those “secret codes” and make fake payouts. See also The Victorian Internet.