in fact it is a different one - but also got a special story... see below 

unfortunately my left hand's tendon problems (from climbing) have increased
couldn't play the fat 57neck anymore and sold it - heartbreaking, I truely loved that bass 

the neck of the bass from the sound example is extremely slim for a p-bass and still playable
thanks Tom 

to be honest, I really like this specific sound - and guess what: 
found it by building a bass with everything I wanted to get rid off to sell it  
but I never had those strings combined with that pickup and neck and made a check for pure curiosity - wow 
 
most important thing: string tension must fit the specific neck/body combination (you can only find out by ear/trying)
string quality and material is crucial 
here it's flatwound strings by Thomastik (JF344) 100 gauge, low tension, very 'wooden' tone
at least one third of this sound is only due to these strings
it'a an expensive brand ... but who cares ? flats keep their shape for ages, those are at least 4 years old
if you're after a more brilliant or typical slap bass sound... it's probably about 4 sets per year 
 
cheers, Tom