yes, you can use the same S3+ firmware for the S3. If your miner has an older firmware prior to October 24 version, please update to the newer firmware such as December 19th version.
Other wise, if your miner is working, please keep it as is!!!
https://bitmaintech.com/support.htm?pid=007201407180243004432lBQW28O0633what is the best firmware for S3+ and S3 ?
do they have the same firmware ?