Sha256 , copy file to new filename

Hello,
i want to create a sha256 hash for a file and copy the source file under new filename as :

sha256hash_sourcefilename

Input : sha256sum FILE
Example : sha156sum mounttest.123
Output HASH_FILE

How to do this ?
e.g.:

e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855_mounttest.123

3 steps :

BaseFile : BF = FILE
HashFile : HF = `sha256sum "$BF"`
Base2Hash : cp "$BF" "$HF"

sha256sum is the command on my UNIX box, gives output as a hash and the file the hash was generated from.

# example using stmt.txt on my box
$ hash=$( sha256sum stmt.txt | awk '{print $1}' )  # use the first part of output, the hash
$ cp stmt.txt ${hash}_stmt.txt