Final Gear and LSD - TRD ?

I want to change the final gear (longer), 

after searching for information, 

I found that the starlet EP86 turbo trans have 3.7 final gear,

same as TRD Final gear TRD(41201-NP110) and match with limo transmission.

and the search begins ....

then i found it from an auction

and that makes me happy is I also get the LSD ... 

I do not know if this is OEM or TRD, but from what I saw the sign is identical with the TRD .. 

this is what i found..

with this TRD from website

so identical .. i hope i got TRD ,, ha ha ..