According to Teichmüller, originally the infantry consisted of 8 companies. Later, a third battalion (never completed) and the sharpshooter company (not part of any of the three battalions) were formed.

End of July 1809, there were the two old battalions, the sharpshooter company, and the understrength "freie Jäger-Bataillon" (battalion of free Jägers, just a dashing denomination):

https://books.google.de/books?id=CDxYAAAAcAAJ&pg=PA21

When the corps was reorganised on the Isle of Wight into 12 companies, probably (I can't prove it) the weak third battalion contributed only three companies.

At that time, the order of the companies was fixed permanently according to the current anciennity of the officers commanding them. That's why the green Jägers became the third company of the regiment,