What happens if a USA tax person invest in Mutual funds as if he/she is a resident

This is a tricky question..I am trying to help an elderly lady who is senior citizen.

She has green card but she travels back and forth between India and USA. She does not want to be in USA permanently but as per US laws she can not stay out of USA for more than 6 months otherwise she can not get a citizenship.

So technically she is called permanent resident in USA hence called US person but in fact after becoming citizen in Dec. 2018 ..she does not want to stay in USA and will return to Indian permanently. After becoming a citizen she does not need to travel back and forth between Indian and USA.

Now at this time (before permanently residing in India) if she invest in Indian mutual funds as resident Indian what are the consequences. Can her investment be blocked by fund house if they find out that she is US person?