This
STR=\"Hello\\nWorld\"
echo $STR
produces as output
Hello\\nWorld
instead of
Hello
Wo
On my system (Ubuntu 17.10) your example just works as desired, both when typed from the command line (into sh) and when executed as a sh script:
[bash]§ sh
$ STR="Hello\nWorld"
$ echo $STR
Hello
World
$ exit
[bash]§ echo "STR=\"Hello\nWorld\"
> echo \$STR" > test-str.sh
[bash]§ cat test-str.sh
STR="Hello\nWorld"
echo $STR
[bash]§ sh test-str.sh
Hello
World
I guess this answers your question: it just works. (I have not tried to figure out details such as at what moment exactly the substitution of the newline character for \n happens in sh).
However, i noticed that this same script would behave differently when executed with bash and would print out Hello\nWorld instead:
[bash]§ bash test-str.sh
Hello\nWorld
I've managed to get the desired output with bash as follows:
[bash]§ STR="Hello
> World"
[bash]§ echo "$STR"
Note the double quotes around $STR. This behaves identically if saved and run as a bash script.
The following also gives the desired output:
[bash]§ echo "Hello
> World"