Education

Yes. I found a source that explains this. If the J-1 short term Visa stay was less than six months, there is no restriction on the new J-1 scholar Visa.

This is not a tax issue but an immigration issue.  Here is an excellent reference source that explains this. once you open up the link, go to table that looks like the one listed below.

12/24 Bars for J-1 Visa Holders

Short term Scholar.