Hello, AyEs!
If you want to transfer from C:\Users\<yourusername>\AppData\Local\AVAST Software\Browser\User Data\Default only bookmarks, bookmarks bar, history, tabs and settings, so you need to copy these files:
Bookmarks (inside of this file is Browser bar config too)
History
History-journal
Current session
Current tabs
And replace files on ypur new PC with these files
If you want also transfer extensions, you will need to copy folder Extensions and replace folder on your new PC with this folder
If this will not work (it can happen if you use ASB for a really long time) - the only advise is to copy-replace the whole folder Default
cus configuration of browser was changing and some parts of files (like extensions etc) can locate inside of different folders.
have a nice day!