A sed solution, mostly to illustrate that sed is probably not the best choice to do this:
$sed -E '1{h;b};/^$/{n;h;b};G;s/^(.*)(.*)\n\1$/\2/' infile
bar
fo
foo
fooo
foooo
sample
Text1
Text2
Text3
prefix
FooBar
BarFoo
Here is how it works:
1 {                   # on the first line
  h                   # copy pattern buffer to hold buffer
  b                   # skip to end of cycle
}
/^$/ {                # if line is empty
  n                   # get next line into pattern buffer
  h                   # copy pattern buffer to hold buffer
  b                   # skip to end of cycle
}
G                     # append hold buffer to pattern buffer
s/^(.*)(.*)\n\1$/\2/  # substitute
The complex part is in the substitution. Before the substitution, the pattern buffer holds something like this:
prefixFooBar\nprefix
The substitution now matches two capture groups, the first of which is referenced by what's between \n and the end of the string – the prefix we fetched from the hold buffer.
The replacement is then the rest of the original line, with the prefix removed.
Remarks: 
- This works with GNU sed; older GNU sed version might need -rinstead of-E
- -Eis just for convenience; without it, the substitution would look like
 - s/^\(.*\)\(.*\)\n\1$/\2/
 - but still work. 
- For macOS sed, it works with literal linebreaks between commands: - sed -E '1{
h
b
}
/^$/{
n
h
b
}
G
s/^(.*)(.*)\n\2$/\2/' infile