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can i connect my Sony TV to my WiFi router using an Amazon Firestick instead of using the inbuilt wireless connector?
No. The Firestick interfaces with the TV only as an HDMI source, for the TV, and the WiFi on the Firestick serves only to feed source material from the internet to the Firestick via the router.
But you can use a Firestick app instead of the corresponding TV app (e.g. Netflix), which will bypass the use of the TV’s WiFi for this app, and replace it with the use of the Firestick’s WiFi.
Though unless you have a 4K Firestick, this would bust your resolution down from 4K to HD, also lose the HDR, and so on.
If you don’t like the TV’s WiFi, though, what you could do is get something like a TPLink Nanorouter, couple it to the Ethernet connection on the TV, and use the nanorouter’s WiFi instead.
As ever, though, in a case like this, it is less a case of examining your conjectured solution than it is of asking the fundamental questions like:-
What problem do you have that you are trying to solve?
What constraints do you have on a solution?
What have you tried so far?