Here is what it looked like to start. Notice the amount that the grips overhang at the front edge, this is absolutely correct for a Luger of this vintage and make.
Here is a shot with the grips removed and the front strap marked at the approximate cut points.
In these photos you can see that I've sectioned the front strap, machined a new piece to fit and I've also machined a welding jig/alignment fixture from aluminum to hold the new piece in place while preserving the frame alignment during welding. The jig will also prevent the molten steel from simply dropping through while welding on the thinner areas of the strap.
Here is the new piece welded in place.
The top weld is filed and polished.
The bottom weld roughly filed up.
All filed up and polished and ready to be rust-blued.
Here is the finished job.