To answer the literal question, you can use a backslash to escape literal double quotes in your command. However, for the reasons given in BashFAQ #50, this is exceedingly poor practice:
# Avoid this absent a very good reason
grep_cmd_str="grep -Po '(?<=Fingerprint=)[^\"]*'"
eval "$grep_cmd_str" <file1.txt # eval is necessary, with all the issues that implies
Better practice when you need to store a simple command (with no redirections or other shell constructs)[1] in a variable is to use an array[2], not a scalar variable, to hold its arguments:
# Use this principally if you need to dynamically build up an argument list
grep_args=( grep -Po '(?<=Fingerprint=)[^"]*' )
"${grep_args[@]}" <file1.txt
If you don't have any constraints that require you to use either of the above, consider a function (which does allow redirections and shell constructs so long as they're hardcoded):
# Use this whenever possible, in preference to the above
grep_fp() { grep -Po '(?<=Fingerprint=)[^"]*' "$@"; }
grep_fp <file1.txt
[1] - Not evaluating shell constructs, in this context, is a security feature: it protects you against malicious filenames or similar content in values which have been substituted into the value you're using as a command.
[2] - Note that arrays are not available in POSIX sh, which your question is also tagged for. That said, similar functionality is available by overriding "$@" (presumably within a limited scope, such as a function, such that its original value is preserved).
