The Chelsea manager is confident that his Cottagers counterpart has the pedigree to keep the Premier League strugglers up despite joining at an awkward time of the season
The Blues were convincing 3-1 winners at Craven Cottage on Saturday thanks to a second-half Andre Schurrle hat-trick, leaving the hosts rooted to the foot of the table.
Despite Fulham being four points off safety going into the final 10 games of their top-flight campaign, Mourinho expects his German counterpart, who was appointed in February, to guide them to safety.
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"I can imagine it is not easy. To go to a club mid-season is difficult; I would like him to survive and start a new season.
"For sure they will fight and get many points."
Fulham have not won in the Premier League since their 2-1 triumph over West Ham on January 1. After that victory over Sam Allardyce's side, the Cottagers have picked up just two points from a possible 24.
On Saturday they travel to fellow strugglers Cardiff City.