I recently switched jobs and started working for another company (Let's call the previous company "company A" and the current company I work at "company B").
Both companies are located in Germany.
I didn't have any job reference from company A upon applying at my current job at company B.
During the interview, we spoke about my tasks at company A. Company B offered me a job after the interview, but didn't ask for any reference from company A.
After I handed in my resignation at company A, I asked for and got a job reference from company A.
On the one hand, the job reference I got from company A is (I think) quite favorable and might underline some of the qualities/qualifications my current manager at company B might not even realize I have, based on the single interview we had.
On the other hand, I don't want to come across over-eager or to give the impression that my previous job at company A was in any way more challenging or rewarding than my current position.
Is it for some reason a bad idea or bad form to hand in the reference with company B, even though they never asked for it?