@blm1028 , assuming that you a US person ( Citizen/ GreenCard ), this would be a gift from a US person ( US will ignore that your mother is also a Vietnam citizen for Us tax purposes ) to a US person. Thus you do not have to file anything ( unless the monies rest in a foreign bank / financial account that you either own or have signature authority over -- for FBAR and/or FATCA regs ). Your mother on the other hand will have to file a form 709 -- US gift tax form , recognizing the gift . It has no immediate tax effect but will count against her gift/estate tax lifetime credit amount.
Can she write check ? Generally no unless you also have a foreign bank account for where the check can be honored --- checks generally cannot cross international boundaries. If she wires the amount to your bank account in the USA, your bank will raise a SAR ( Suspicious Activity Report ) as a general practice and generally nothing happens -- US treasury requires this for all activities ( international ) for amounts > US$10,000. Note that high amounts like a million or more may require US Treasury approval for incoming while the outgoing country may also have restrictions / foreign exchange controls ( even if the amount is from a US $ denominated account locally held.
Is there more one of us can do for you ?