Question about Gigaset E560 HX (CH-Version)

You cannot simply replace the defective handset of your Duo version with the E560 HX (CH version) offered here, as this is a DECT handset designed for operation with routers or DECT base stations. The E560 HX is not an analogue handset, but a cordless DECT phone, while your Duo version is presumably an analogue landline phone. It is therefore not compatible. For a replacement, you should use an identical or compatible handset from the same Duo series.