@Mirka1 NO that is not true . Once you have become a US Person ( citizen / GreenCard / Resident for Tax purposes ), you are required to recognize your world income and be taxed by the IRS on it. Thus if the sale/ disposition occurred after you became a US person, that transaction need to be recognized ( reported ) and be taxed , even if it has already been taxed by the country where the asset was situated.
Please recognize that the penalty for non filing of a return / failure to pay taxes,/ failure to file FBAR and FATCA forms are very onerous. Please follow the laws and truthfully so.
Monies transferred to the US and deposited in a US bank account, falls under treasury rules and any amount over US$10,000 will generally cause the bank to raise SAR ( Suspicious Activity Report ) as a matter of course and usually nothing happens -- larger the amount more likely to draw US treasury attention.
Is there more I can do for you ?
