Close.

#!perl
use strict;
use 5.010;

local @ARGV = 'myinfo.txt';
local $^I   = '.bak';

while( <> ) {
    s/^Author:.*/Author: Johny5/;
    s/^Phone:.*\n//;
    print;
}
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And since you're already requiring 5.10 (for no reason), you might as well use \K

#!perl
use strict;
use 5.010;

local @ARGV = 'myinfo.txt';
local $^I   = '.bak';

while( <> ) {
    s/^Author: \K.*/Johny5/;
    s/^Phone:.*\n//;
    print;
}
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