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You could use awk like this:

awk '
FNR==1 { file++ }
/^Package: / { p = substr($0,10) }
/^Version: / { v = substr($0,10) }
/^SHA256: / {
c = substr($0, 9)
if(file==1)...

Assuming you already have the two file locally (you will need to fetch FileA from the web server using something like wget).
Also that the SHA keys are a string of 64 hex digits (0-9 a-f) which...