Prince Philip advised Harry to pay attention to Meghan, saying, "We go out with actresses, we do not marry them," they say.
Philip, 98, would have said this remark to his grandson while the relationship between the two men became serious.
But Harry, 34, proposed and tied the knot with former actress Suits, 37, last May.
The Duke of Sussex and the Duke of Edinburgh are known to maintain a very strong relationship.
Last week, Instagram accounts of Harry and Meghan wished a happy birthday to "Grandpa".
Philip was also featured in one of the couple's first shots, the baby Archie, alongside 62-year-old queen and mother of Meghan, Doria Ragland.
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The Duke was actually one of the first people to see the tot, as Meghan revealed during a brief interview in a photocall.
She said, "We stumbled upon the duke as we walked by, which was very nice."
Philip also made a surprise appearance at their royal wedding, although he had recovered from an operation at the hip at the time.
This is not the first time that he gives advice on marriage.
In 1997, he said, "Tolerance is the essential ingredient. You can deduce that the queen has the quality of tolerance in abundance.
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The alleged remark appeared in a Sunday Times Magazine article by Sophie Money-Coutts.
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