I don't do it any more but I used to lay an oversized piece under original then stitch all the way round twice either side of weld then cut out old piece after just to keep it true . it was always for the trade but prefer to talk customer in to complete new roof now . you get what you pay for

From what I've been told, there's no way to replicate the factory heat seal and trying to glue it in won't work because of the tension on the back window. You can't guarantee it will hold, let alone, leak. I've talked with Electron Tops, Doug Robbins of Robbins Tops and others. They all said the same thing. I was told the heat seal process was a 2-3 day process. So, I turn those repairs down and try to talk them into a new top (or at least a back window unit if it's a 2 piece top)

Repairing a damaged one piece top requires removing the top from the top frame and then sewing in a new rear curtain without scratching the plastic. After the curtain has been replaced you have the task of refitting the top.

Here is the rub- The old top has been exposed to the elements for a period of time and most likely will not fit exactly as it did originally due to shrinkage. The repair to the curtain will look like a repair and it will be very noticeable to everyone. The cost to the customer will be near the cost of fitting a new top.

Our industry needs to step up and become more professional in our approach to the service we do for our customers. It will benefit the customer in the long run to have a new top installed- clean look, leak free and it adds value to the car and carries a new top warranty. As an auto trimmer with the resources to obtain a new top, repairs to an old one piece convertible top is not a money maker, but rather busy work.

@Amelia Brooker

The window in the picture is not glued. These windows are welded in a high frequency melting process. Seamless glued windows are very rare (at least with the European manufacturers). The Audi 80 and the Fiat Punto had such windows with the distribution. There was a kind of hot glue under in the window frame in which a copper wire was built in. You had to connect 12V to the copper wire to melt the glue for the installation and removal. For the installation one needed an original inner and outer frame to melt the new (mostly cursed expensive) windows in exactly the same way again. But even with the original frames, it didn't work with at least one of 5 windows. Because the wire at the start and at the end was hotter than in the middle. Either the window wasn't glued in the middle or - in the worst case - the convertible top was burned at the start and at the end.
With the welded windows as you posted them I sew in the new windows. But since the top has to be dismantled, you have to analyse the situation and condition of the soft top beforehand and talk to the customer about his car.
Of course, it is important how long the customer wants to drive the car? But even more important is how do you estimate the condition of the entire top. Have seams already dissolved? Are rubber bands or assembly strips damaged? You must be able to dismantle and mount the top without damage. Every customer thinks his top is "still good"... You have to stand up for it afterwards. Replacing the window is not worthwhile if the top is broken after one year.
I do it mostly in such a way that I ask the customer how long the window has lasted. And if I am of the opinion that the convertible top will last this time again, then I sew in a new window.
Also you should look what a new top costs. If it only costs a few hundred dollars it doesn't make sense either. Because the customer already pays the assembly costs - and in addition the material and the time for the sewing in or smaller repairs (1.5-2.5h) come still in addition.

The sewing is done as follows:
First I make marks on windows and window frames (the 2cm welding track). Then I cut out the window pane. I put the old pane on the new window pane.
You can also fix it with double-sided adhesive tape. But the tape must be removable without residue. I cut the new window to size beforehand but left it slightly larger.
Then I fix the top on the new window and make sure that the lines match those on the old pane. Then I sew in the window again with a special piping for windows (used at BMW Z3 for example). The piping has the shape of a "J" in the lateral profile so you don't look into the cut edge of the canopy fabric anymore. You should place the attachment of the piping in the middle of the window at the top, so that water can run in at the edge.

I hope you understand the translation :D

I try to post an pic of the piping tomorrow.

For plastic windows the new window must be sewn in then the old one cut out. On glass windows we use quick set 2 part epoxy and 2 people. We glue about 6" at a time, securing it by hand and waiting for it to set. This can quite easily cost many hundreds and is usually done for smaller separations.

I have been using 3M window weld after of applying a coat of 3M glass primer. Then I release the top at the header and prop it up. I hold the repaired area together with strong magnets and steel walk away and let it dry a day.
But if epoxy holds your way is quicker.

Thanks for all of the advice everyone! That's the only way I could think to repair it too. I agree it's not an ideal solution. They just replaced their top in the last few years but didn't quite get it in storage before we had snow so the window cracked. Hoping to help them out so they don't have to have the entire top replaced again! Thanks for the advice!!

here are the promised photos of the repair option with the Piping

@Jens Jesberg Thank you that's very helpful! Where do you get that piping from?

@Amelia Brooker
I'm getting it from the MAH. But I think one of us will also know a supplier in Canada or USA where you can get it. But MAH certainly also ships internationally. If you don't get it tell me I have at least 70m left on the roll.