Bad service during my DSL activation .

From the picture, If the TAE looked like that after installation, it must have been loose before as there doesn’t appear to be any proper fixture. Telephone lines are very low voltage, so the risk of electric shock is almost non-existent. Nevertheless, yes, it should not have been left like this, but as you correctly pointed out the technician comes form the Telekom so the only thing o2 can do if you want is to request that someone comes and pushes it back into the wall.

O2 charges the fees for the Umzug to provide a perfect service . If the TAE is loose or not this is of course not my problem this is the problem from the Techniker . Unacceptable to pay 50€ for this kind of service. Of course I am waiting for an answer from O2 side ! 

More than that I took the picture exactly the time when the Techniker left so time and date can be proven . 
 

By the way replying to other people questions doesn’t look good.

If you do not want to push the TAE back into the wall yourself, call customer services and request a new appointment. If you want to complain about the Telekom technician, send in a letter of complaint.

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Whose questions am I supposed to answer then? My own? You realise this is a discussion forum, right?

In the apartment is provided flush-mounted box, that's why the hole in the wall. The flush-mounted box must be installed by the owner, matching the rest of the switch / box series in the apartment. There should actually be a double frame for power socket and TAE socket. However, as already mentioned, the flush-mounted socket is the responsibility of the owner.
The telecom technician only has surface-mounted TAE boxes with him. Of course, the technician could have screwed the surface-mounted box to the wall, but the hole in the wall for the flush-mounted box would still remain. 

I therefore assume that the technician has recognized that a proper looking solution can only be done by the owner and has therefore refrained from drilling 2 additional holes in the wall as a temporary solution. The 2 holes would have remained visible even after the installation of the flush-mounted box, which would not have been a good idea.

The telecommunication cables do not pose a risk of electric shock, as the cables are insulated and the stripped parts of the cable are inaccessible in the TAE socket.
With DSL connections, however, there is practically no measurable voltage on the lines any more anyway.