A damage purse strap
Q-Tips
E-6000 Glue
Make sure your well vented area.
Lay the strap flat on a table
Using a Q-tip to apply the E-6000 to the break in the leather carefully.
Wait, I waited 24 hours before moving the strap and another before use.
Its not the prettiest repair in the world, but its holding much better then resewing it back together.