Spread 1/2 cup refried beans onto half of each tortilla, sprinkle with shredded cheese. Add tortilla one at a time, to hot skillet. Fold over in half and heat until golden. Flip over and cook until golden once again. Remove and slice into triangles. Continue until all bean quesadillas have been cooked. Allow to cool if packing into a lunch box.
Slice avocados open and cut into cubes.
Add quesadilla triangles, cubes of avocado and strawberries to each lunchbox container.