You are using input #150? Note that it is not a physical input on an FMD PLC, but it can be used as an internal flag for the ladder program to control something. So yes you can read and write to it and it will keep its last logic state written by the Modbus client.
When you write to Input #15 - this is a PHYSICAL INPUT. What is written to the PLC's input will only exist for less than 1 scan time because af the end of the ladder program the PLC will update the physical inputs and outputs and thus the INPUT #15 will be overwritten. We do not recommend writing to the physical input as it may or may not activate the circuit that is waiting for it to be set to "1" - it depends on when the input is written relative to the rung of circuit in the ladder program.