Challenge: Keep the telegraph relevant!

Nuclear war wipes out over half of the cities in the 1980's.
With every telephone line destroyed and the telephone infrastructure destroyed by EMP, the world is isolated. In the struggle to survive and remain in contact with each other, telegraphs are put in place as a stop gap measure.
Amongst the few surviving military bases of North America, the internet survives. Using it the military begins to coordinate and attempts to rebuild civilization. To help with this task, the few remaining computer programmers create an instant messaging program allowing the generals to remain in constant contact.
 
Now this may be totally ASB, but if the British financial crisis of the post war era was even worse than it was in OTL, could it be possible that the General Post Office would have maintained the telegraph network at least until the 80’s?
 
Bonus points if the Internet stays as well; double bonus points if e-mails and IMs remain.

It's remotely possible that following a nuclear war or some other form of global disaster that undersea telegraphs might be used as a form of low tech long distance communications, especially if radio was completely un useable. (Simple undersea cables of intercontinental length can only really be used for Telegraph signals.) The basic technology is well over 100 years old and is unlikely in my view to be lost.
On land I can't see why simple telephones or possibly electromechanical teletypes wouldn't be used instead of telegraphs.
As a side note in the late 1990's when I was ordering an intercontinental private line circuit for a major company, a telecommunications company presented an order form to me that listed a telegraph circuit as an available product.
 
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