Visit recursively all files in a folder and insert a specific string

[Hannibal2010]

Dear all,

I have the question that:

I have a directory in Linux, call it: test_directory.
This directory has files and sub-directories. (only text files)
Text file CAN contains the specific string, for example, MY_STRING_1
For example, one line in one text file maybe:
MY_STRING_1 abc xyz blah blah //MY_STRING_1 is not single word in one line.

Now, I want to access ALL files in this directory (include sub-directories) and after each MY_STRING_1, add MY_STRING_2 as new line.
For example:

MY_STRING_1 blah blah blah
abc xyz

will become

MY_STRING_1 blah blah blah
MY_STRING_2
abc xyz

Please give me a help. I am using Linux environment