LONDON — Prince William and his wife Catherine have been filmed at a farm shop near their Windsor home, The Sun newspaper reported — the first footage of Kate since she had abdominal surgery for an unspecified condition two months ago.

The newspaper published a short clip late Monday that appeared to show William and Kate smiling as they walked together, carrying shopping bags. It said the footage was taken on Saturday in Windsor, west of London.

The Sun quoted Nelson Silva, who said he filmed the video, as saying, “Kate looked happy and relaxed. They look happy just to be able to go to a shop and mingle.”

The couple’s Kensington Palace office did not comment.

The palace has said Kate, 42, will return to official duties after Easter. That’s likely to be once her children go back to school on April 17.

The Sun plastered its front page with “Great to see you again, Kate!” It said it had decided to publish the footage “in a bid to bring an end to what the Palace has called the ‘madness of social media.’”

Feverish and at times fantastical speculation has swirled about the princess’s condition during her absence. The palace has not disclosed details, but said it is not cancer-related.

Kensington Palace released a photo of Kate and her children George, Charlotte and Louis on March 10 to coincide with Mother’s Day in the U.K. But the move backfire when The Associated Press and other news agencies retracted it from publication because it appeared to have been manipulated, fueling even more conjecture.

Kate issued a statement acknowledging she liked to “experiment with editing” and apologizing for “any confusion” the photo had caused.