[Grammar] "crossing" and "having crossed"

[xxwzs]

Here comes a question:
In 1861 John Stuart successfully crossed Australia. Ever since he has been famous for ______ the continent.
A. crossing B. having crossed

I deem both A and B as acceptable keys. But I don't know why.
So what about your view point?
Thanks.

 

[emsr2d2]

They both work in BrE.