Another_CFI
Unfortunately, I don't think that's correct (at least in UK). I don't have the EASA ref to hand but CAA Standards Doc 14 says (Section 8.4)
"An IR associated with a single pilot high performance complex aeroplane is type specific and does not automatically confer IR privileges in other-single pilot aeroplanes. However, credit may be available towards the IR section of a proficiency check in another type or class of single-pilot aeroplane."
There's a flowchart at the back that illustrates (!) what extra needs to be done to revalidate the generic SP IR but if it's lapsed (ie renewal rather than revalidation needed) then there's no credit and you have to do the full LPC.