To cancel your o2 DSL contract at the agreed end of the contract, please complete the cancellation form, sign it and send it to o2 by letter or fax.

Thank you for the cancellation form. 

I would like to cancel o2 my home S DSL internet plan at end of the contract duration. After that I would like to make a new monthly DSL internet contract (o2 my home L). Can I have the router which I got from o2 for the my home S plan and used it for my home L? Are the router same for both plans?

I can only advise against this approach. A tariff change from a fixed-term contract to a flex contract is not offered by o2. 
When ordering a new o2 DSL connection, you will therefore receive a new telephone number and the connection price of 69.99 EUR will be charged. Since you are not a new customer, you would not receive any new customer discounts.
Routers from o2 must be returned to o2 at the end of the contract. If you want to rent a router again together with the new Flex contract, you will be charged 49.99 EUR provision fee, 9.99 EUR shipping costs and the monthly rental fee for the device you want.
If you cancel your existing connection and then order a new connection, you have to expect an interruption in the supply of Internet and telephone services that may last for a longer period of time. 

Actually I am moving from berlin to Salzgitter. So I ordered a o2 move today. But I selected a option to extend the contract till it's duration that is 23.7.2021. it will cost me 49,99 euro service charge. Am I right? Can i now update to o2 my home L and as well extend it for 24 months?

Can I still do this change? Because I submitted move today

I would recommend to change the tariff to o2 my Home L after you have moved to your new place. This way you can see what speed is actually possible at the new address. The price should be similar, as there is only one discount: Either a discount on the moving fee or a discount on the new tariff. 

Hello @siva123,

were all your questions answered? Or is there still something unsure were we might to have a look into? :-)

Regards,

Lars