Interesting question, and no easy answer. Are Tele2 your ISP (simply internet access over DSL), or your DSL provider, or both? You might not even know the answer to this, as many ISPs hide the fact that over a longer period they will transfer your DSL provision to themselves (via Tkom reselling)
To answer your question:
- If Tele2 are simply your ISP - advising Telekom that your number and DSL are to be transferred will be sufficient. You should also tell Tele2 you moved, but this is not critical
- If Tele2 are your DSL provider - Telekom will not be able to move the DSL component of your line (and should tell you so, so this is a good hint when you ask for your services to be transferred!). You will need to tell Tele2 you are moving. They will need to co-ordinate this with Telekom. Don't hold your breath on this. Tele2 need to cancel their contract with Telekom on the old line and start a new one on the new line once established, even though it's the same number. This can take 7-10 days (minimum!) to organise.
One hint - if the current Tele2 offering is cheaper than the one you currently have as DSL offerings often are, negotiate for the new rate - in principal at least, your house move is cancelling the old contract so you are entitled to the benefit of new conditions.
YL6