Pretty sure it's been the case since long before then. If you read Jane Austen novels, it's pretty clear that w/in London it was possible to send notes back and forth with only a 1-2 hour latency, sometimes less.
Or consider the following quote from That Hideous Strength, written and set in the mid 1940s; the "Bill" in question has recently been murdered:
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"There's a letter you wrote," said the Fairy.
"What letter?"
"A letter to Mr. Pelham, of your own College, dated six weeks ago, in which you say, 'I wish Bill the Blizzard could be moved to a better world.'"
Like a sharp physical pain the memory of that scribbled note came to Mark. It was the sort of silly jocularity one used in the Progressive Element -- the kind of thing that might be said dozens of times a day in Bracton about an opponent or even about a bore.
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If that scene was written now, the message in question would certainly have been a text. Email is certainly much more convenient than snail-mail or inter-departmental memos, but people have been writing short, quick notes to each other for millennia.
NB a few minor edits.