set custom avatar only for 1 user

If you’re only concerned with your own profile, you could register at https://gravatar.com (yes, that will run through wordpress.com, don’t be surprised). Use the same email address as your admin account uses and put the image you want there. After that it will be used by your wordpress wherever a profile picture should be displayed.

This will work as long as you don’t use a plugin that disables Gravatars.

One more hint: the plugin you used “WP First Letter Avatar” is extremely old. Unfortunately I can’t judge how compatible it is with Gravatar images. Normally I would advise to ask their support, but I don’t think it exists anymore. Maybe you should look for an alternative.

Is any snippet code for set custom profile picture for my admin account?
For example: if username is (admin) then set a custom url as avatar

You could try one of these:
https://gist.github.com/nfsarmento/c96a95a8cc5154398d773090b9ea9909#file-functions-php
https://gist.github.com/spigotdesign/4716763

This adds a meta field to the user that contains the link to the image. How you then display this in the frontend of your site depends on your theme and also requires individual programming there.

tnx