Hi karl - Good spot !
The Service Manual calls for T3880620 - Described in the Parts listing as as "Socket 48mm",
and in the Service Manual as "Adjuster Socket, 48mm", for the Castellated Lock Nut
and the Adjuster Nut, when adjusting the Trophy Headstock Bearings.
The same tool is also called for in the Service Manual,
for the Rear Bevel Box right hand pivot pin locking ring.
T3880023 (50mm ) is, as you say, listed as a Service Tool for the Trophy
but I haven't ( yet ? ) found any reference to it within the Service Manual.
T3880023 is listed as a Headstock Bearing Adjuster socket for other Triumph Models,
and I found one reference from someone that ordered one for their Tiger 1050
only to find it was the wrong tool - incorrectly listed !
It is
possible that T3880023 should not be listed as a Service Tool for the Trophy.

