No, it won't.
That's partly because when you do this:
Form1 fm1 = new Form1();
It creates a new instance of teh form, not accesses the instance that is displaying.
It's a bit like cars: if you put your mobile phone in the glove box of your car, then buy a new one - would you expect to find your mobile in the new car glove box?
You need to access the existing instance of Form1, not create a new one.
But...the better way is to get the existing instance to do it for you...
Depending on the relationship between the forms, have a look at these:
Transferring information between two forms, Part 1: Parent to Child[
^]
Transferring information between two forms, Part 2: Child to Parent[
^]
Transferring information between two forms, Part 3: Child to Child[
^]
Judging from the names, you probably want part 2.