The Citizen Advice is correct, CB ESA is an indefinite award until you are next assessed and either placed in the support group, WRA group or found fit for work.
As you state that you have just had your CB ESA extended for two years I assume that you have been placed in the support group.
Unfortunately I do not have all the facts whereas when you saw the Citizen Advice they are able to ascertain all the relevant details.
Regulation 19 of the UC (Transitional Provisions) Regulations 2014 make it clear that those who move from ESA onto UC (and have not been found fit for work), are to have the LCWRA Element included in their UC assessment from the start of their UC award if they were in receipt of the support component in their ESA award.
This means that the work capability decision must be transferred across from an ESA award to a UC one.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems