HB appeal

Hi. My client was out of the country for more than 4 weeks. She told the DWP who suspended her ESA (cb and ir) until she provided reasons and ticket documents. Her reasons were accepted and claims put back in payment . HB / CTR stopped at same time of ESA suspension because of her absence exceeded HB limits and they have refused to put it back into payment at MR so appeal rights offered. I am slightly baffled as I expected them to follow DWP direction, she wasn’t away for an extraordinary amount of time. Clock is ticking and rent not being paid - I don’t want to encourage the appeal if it’s refused, she wants to avoid claiming UC.
What is the rule here?
Thanks in advance