Ok, I have found the Manual for the Linn Classic Movie.
I had thought that the Linn was some kind of AV Amp, but it turns out
just to be a Glorified DVD Player.
I assume you have other Classic Movie units in the House connected
using the "Connect" Feature.
That would explain the wording in Post #1
The unfortunate thing seems to be that the Linn doesn't have any Digital
inputs, which is why your Optical Cable doesn't work.
All the inputs on the Linn are Analogue.
Having looked at the Manual for your Sony Bravia, you only have Two Audio
outputs available.
1. Is the Digital Optical output you have already found, but which cannot be
connected to the Linn directly, because the Linn doesn't have a Digital Input.
2. The Headphone Socket, which is essentially an analogue Audio Output.
The HDMI connectors on the TV are inputs only, so are only of any use to you
if you wish to feed Audio into the TV, not the other way round.
So, as I see it, you have Two options.
The cheapest and easiest, is to connect the Headphone Socket output on the
TV to the Audio input Pins on the SCART connector on the Linn.
This will require you making up or buying a suitable cable.
Alternatively, a better solution would be to buy an Optical Digital to Analogue Converter like this one:
https://www.ebay.co.uk/itm/DAC-Conve...gAAOSwbs5fvERo .
There are others available, but this is the first one that came up on my search.
So in answer to your original question, it is not an HDMI Converter you need.
Maybe others might want to confirm if they agree.
Ian