hyperlink and vlookup in the same sheet

Judging by the images I'm not quite sure you understood the point I was making.

The VLOOKUP will only return the friendly_text associated with the hyperlinks (or where omitted the address)
You must therefore ensure that you can reconstruct the hyperlink from the friendly_text value (or if omitted the address!).
If you can not then you can not return the hyperlink to your 2nd sheet via formulae.

You said you could not get my suggestion to work... using your images, the hyperlink for Agito would be:

=HYPERLINK("#Sheet1!B11")
etc

Your formula in 2nd sheet would then be:

=HYPERLINK(VLOOKUP(B3,test,2,0))

Point being by omitting the friendly_name the HYPERLINK will be default use the Address... you can in turn encase the VLOOKUP result (address) in a Hyperlink function.