Good news. I have successfully use Pico Micropython to transmit a message from FS1000A and receive the message from MX05V. However, the xmit/recv is not reliable. The complete listing is shown below:

# simplePicoRfV10.py  tlfong01  2021oct28hkt1150
#
# Pico GP Pin Assignment
#   GP0 = UART0 TxD = FS1000S
#   GP1 = UART0 RxD = MX05V
# Setup
#   1. To loop back, short TxD pin to RxD pin
#   2. To test Xmit/Recv, connect GP0 pin to FS1000S (Note 1), GP1 pin to MX05V
# Note 1
#   Warning: Pico 3V3 Gp0 pin direct connecting to 5V FS1000S data pin, might cause "latching up", and fry Pico (5% chance).
# Note 2
#   Suggestions
#   1. Use HCT125 or HC03 to shift 3V3 logical level to 5V.
#   2. Use 12V to power FS1000S to increae xmit power and therefore longer effective distance

This is another sample output:

>>> %Run -c $EDITOR_CONTENT
Begin testXmitRecvV09(), ...
  bytes written               = b'\x00x5b\x00xb5\x00x5b\x00xb5\x00x5b\x00xb5\x00x5b\x00xb5'
  bytes read                  = b'b\x00xb5\x00x5b\x00xb5\x00x5b\x00xb5\x00x5b\x00xb5\x00'
End   testXmitRecvV09().
>>>

This is the layout of the devices. I have no HCT125 in hand, so I just use the HC04 Hex Inverter instead. The HC04 is powered 5V, but the input is 3V3 from Pico GP0 (uart0 TxD). HC04 inverted 3v3 signal twice and shifted 3v3 to5V, and results is satisfactory.