In a medium saucepan filled halfway with boiling, salted water, cook the green beans until crisp-tender, about 5 minutes. Rinse with cold water.
Slice the pork crosswise 1/4-inch thick. Transfer to a bowl, season with 1/2 teaspoon each salt and pepper and toss. Sprinkle with the flour and toss again.
In a large skillet, heat the olive oil over medium-heat. Add the pork and cook, stirring, until just no longer pink, 4 to 5 minutes; transfer to a plate. Add the shallot and cook, stirring, for 1 minute. Pour in the wine, bring to a boil and cook until reduced to a syrup, about 3 minutes. Pour in the broth and boil until reduced by two-thirds, about 4 minutes.
Return the pork to the skillet, add the green beans and rosemary and cook, turning, until heated through and the sauce is thickened, about 2 minutes. Stir in the strawberries and sugar; season with salt and pepper.