In a congratulatory phone call, Britain's Iron Lady confided to Clark that the keys to her initial success were forming a "well-balanced government" and making decisions only when she was ready.
Thursday marks the 35th anniversary of Clark's short-lived victory over Pierre Trudeau's Liberal party.
As 1979 drew to a close, Clark's minority Progressive Conservative government fell on a non-confidence motion, opening the door to Trudeau's return to power in March 1980.
But all that seemed unthinkable on May 23, 1979, as Clark credited Thatcher's Conservatives — who took office just weeks earlier — for helping steer Canadian voters to the right.
"There's no question that your victory paved the way for ours," he told her.
"Well, I did hope that," Thatcher replied. "You know we've been watching it anxiously in the last few days and I just hope that we might have been able to help a little. But the great thing is that the tide is moving all over."
Clark said he would welcome any suggestions from the fledgling British leader, as she seemed "to have been doing very well."
"You just get stuck in, that's all," Thatcher said. "You have to get stuck in and really rely on your own instincts."
Thatcher suggested she moved to temper the tone of her government by balancing the "fervent believers" in the Conservative fold with more moderate voices.
"But apart from that, all I did was just get on, but never take a decision before I'm ready to."
A transcript of the brief telephone conversation was among records on Canadian affairs unearthed in Britain's National Archives by The Canadian Press with the help of Steve Hewitt, a senior lecturer in Canadian and American studies in the history department of the University of Birmingham.
The friendly atmosphere of the phone call is a display of like-minded politicians "slapping each other's back," Hewitt said in an interview.
In a brief phone message, Clark said Wednesday he was pleased to recall the chat "all those years ago" with Thatcher, who died in April 2013.
During the 1979 call, Clark said he had a "very good group of people and I think we have won a significant victory" — despite winning just two seats in Quebec.
"We have a problem still in Quebec but that is something we can overcome."
Thatcher offered encouragement, saying "once you're in office it makes the world of difference."
"You have all the authority you haven't had before."
The British leader heaped praise on Clark, hailing his "famous victory," calling his comments on the radio "superb" and declaring her office "very thrilled" at his success.
Her remarks stand in contrast to the rather chilly relationship she would later develop with Trudeau, who had different ideas about foreign policy and involved Thatcher in the sometimes messy effort to patriate the Canadian Constitution.
In a declassified British telegram from February 1980, Sir John Ford, high commissioner to Ottawa at the time, made the Thatcher government's sympathies clear.
"For all its inexperience the return of the Clark government ... would, I believe, be in our and the (United States') best interests as well as Canada's," Ford wrote in the confidential note to various departments, including Thatcher's office.
Any "overt action" to help the Clark government would be counter-productive, but anything Thatcher could do to show appreciation for Clark's "robustness" on global issues, including his support for a boycott of the coming Moscow Olympics, "would be helpful," Ford added.
The following month, the Liberals — under a revitalized Trudeau — won a majority government.
Clark said Wednesday he had not seen the memo before.
It was unrealistic to think any comments Thatcher might make could really help Clark, Hewitt said.
"It was a bit of an inflated notion to think that that could sway the Canadian electorate."
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