What Happened To This Stamp?

I found a very unusual defect on this Germany Allied Occupation stamp. It seems that at some point paper went through something similar to "printer paper jam" - it was partially folded. As a result stamp lost about 0.8mm width (comparing to normal) and one tooth in horizontal perforation (normal stamp has 15 teeth, but this one only 14). It is also lost one letter on top ("DEUTSCE" instead of DEUTSCHE). All that is not unusual except the fact that something happened after paper jam. It looks like the stamp was pressed (and possibly even "baked") so hard that folded area become completely flat and smooth on both sides (see image).
However, paper thickness is uneven, it is almost double along folded area (~0.13mm instead of normal 0.075mm).
Another observation: cancellation is not very clean, but most likely all those events happened before stamp went through a post office. I hope somebody could help with explanation. Thanks.

It looks like the mailer tore the stamp incorrectly and managed to make a slight overlap (almost 1 perforation width) when applying the pieces to the envelope, which then passed through the mail.

But in this case it will be easy to separate both parts again. With this stamp it is absolutely impossible - paper is smooth and inseparable.

Opinion.
Agreed,
The stamp has been torn and repaired, rather poorly.

I have to agree with you after looking under microscope. However, it was not a poor job - it was rather amazing job! I soaked this stamp and it survived perfectly. Somebody used an excellent glue and probably hot pressure, because I cannot even feel overlapping area - it is so smooth.