SPOILERS********
Those that downvoted as the police were made to look stupid or that murder isn’t a joke, missed the whole premise of the series.
This is how the two murders saw the world, their world, not ours, not the polices but who they both viewed their lives.
The husband told his MIL but believed she wouldn’t tell, they communicated via email with the police and asked for an extra few weeks and if they could pay for the train trip, husband didn’t want a free lawyer, they kept responding and getting pensions for a man who turned 100, husband believed Gérard Depardieu was writing to him, they worshipped the old Hollywood stars pictures autographs, whilst not being able to eat.