Prince William sent a message to Doris Hancock as she reached the halfway point in her walk along Hadrian's Wall.
The 95 year old from Ambleside is doing the walk to raise money for the charity Centrepoint.
The Prince's message was read to her by one of the charity's members.
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John Davidson, who grew up in Newcastleton, was killed while trying to arrest a suspect last week.
Police are looking at CCTV footage after money was taken from her bag in a shop in the town.
Four other people have been released without charge, after Kevin Slater was found dead outside a property on Borland Avenue.