auto shift on keypad press in lcd using fujitsu F2MC-16LX MB90385 Series
The normal method of using the HD44780 type lcd is to shift the cursor to the right after every character entered.

Instruction     RS  R/W DB7 DB6 DB5 DB4 DB3 DB2 DB1 DB0
Entry mode set  0   0   0   0   0   0   0   1   I/D S



  Sets cursor move direction (I/D), specifies to shift the display (S). These operations are performed during data read/write.


Bit Settings
I/D 0 = Decrement cursor position   1 = Increment cursor position
S   0 = No display shift            1 = Display shift


Your entry of 0x06 (0b110) sets it to Cursor Shift Right (Increment). If you change it to 0x07 (0b111) it should set it to shift the display right while the cursor stays in the same spot. I believe this is what you want (Characters fill in left to right). So like 0, 10, a10, etc. Shift left (0x05) and it should be 0, 01, 01a, etc.