Nobody has ever won both these titles in the same year.
When you consider that the Ladies' British championship has been played 113 times since 1893, Julia has already proved to be a very special young talent.
That victory at Dundonald Links, achieved against a field of all ages and established international players, makes Julia the favourite to show her class against her Under-18 girls' peers at the classic Welsh links venue this week. Does that put her under a lot of pressure to produce her peak form?
Not a bit of it. Speaking in the Royal St David's clubhouse, Julia said: "I am at the stage of my golfing career when I play the game for fun. I am hoping to have a fun week here in Wales.
I can only try to play my best but I hope to enjoy myself whether I win or not.
"There are a lot of good golfers from all over Europe playing in this championship and they want to win too! Winning titles is good but having fun and enjoying the experience is just as important for me."
Miss Engstrom, a member of Ringenas Golf Club, a 27-hole complex near Halmstadt in Sweden, comes from a golfing family. Her father has four of a handicap, her mother a lot higher - but "she plays for fun." So that's where Julia gets her attitude to the game!
Julia was given a plastic golf club to swing when she was two years old and the rest is history! She now has +4.2 of a handicap, having started the 2016 season with a rating of around +2.7.
"I've had a terrific year. I've played in the US Women's Open in California, the Ricoh Women's British Open at Woburn and I still have the Evian Championship to come in France," said Julia.
"I've loved the atmosphere at these majors. That's what attracts me about the prospect of turning professional a few years from now."
With her CV, Julia is sure to have the US college coaches - and there are plenty of them in attendance at Harlech - seeking to offer her a golf scholarship .. but they are restricted by NCAA rules and she is too young at the moment to be approached by them.
"I have a USA college scholarship on my list of possibles for when I am 17 or 18," said Julia. "But it's not a 'must' for me at the moment. There are good universities in Sweden but it's a decision I don't have to make for another two or three years yet."
So what holds the key to Miss Engstrom completing a trail-blazing British titles' double at Royal St David's GC this comng week?
"I would say my ball-striking. I don't think any part of my game is more outstanding than the rest. But my ball striking will have to be at its best to succeed here."