MIxed age UC claim both LCWRA - can either claim carer element/allowance for UC/Council Tax Reduction?

I have a client with terminal cancer who lives with his wife.  He is 66 and has just started receiving state pension. 
His wife receives contribution-based ESA Support group.  They are claiming UC and receive a LCWRA element in calculation.  They both receive maximum DL/mob PIP. 

Can wife claim carer element in UC (as husband would count as LCWRA by virtue of his PIP and being pension age?)  Or can’t she do this because she is on ESA?

Even if not, should she claim carer’s allowance which she wouldn’t receive due to overlapping benefits rule in order to claim a carer element in calculation of council tax reduction?

When I try to use QBC benefit calculator it just flashes up a warning “The rules are ambiguous” which doesn’t help much.

Can anyone help?

I think she can ask for the carer’s element to be included in the UC award, the conditions are that you must provide care for 35 hours or more a week and the cared for person must receive either DLA (middle or higher rate care component), PIP (daily living component) or Attendance Allowance. The fact that CA and c-ESA would overlap is neither here nor there.

She can’t get a carer’s discount from the CT liability as she’s caring for her partner, you’d need to check the rules for the CTS scheme locally to see what the conditions are for a carer’s element to be included.

should she claim carer’s allowance which she wouldn’t receive due to overlapping benefits rule in order to claim a carer element in calculation of council tax reduction?

If they are on UC without earnings, they will get 100% of whatever maximum the local working age CTR scheme allows in 99% of local authorities.  CTR does not have a conventional applicable amount in such cases.

thanks all for your help with this