I m not an expert on these but based on my conversation with my tax consultant, an amendment is needed only when there is a change to your income or deductions. IRS has very specifically instructed on the process of changing ITIN to SSN by sending a letter to IRS Texas office requesting them to update the records. I have already mailed them the letter. Below is the process
https://www.irs.gov/individuals/additional-itin-information
