Hi Rom@n,
I think Below steps can help you :-
1) Take one TextBox when 1st user submits or saves the form then fill a Value in the textbox like - [ Already Filled ] .
2) Create one more - View form Design Tasks >> Views [i.e View 2] Copy Paste Controls form View 1 to View 2.
3) In View 2 Properties Check Read Only Check Box. So now your View 2 will be a read only view.
4) Go to Tools>>Form Options>>Open And Save >> Go to Rules Tab.
5) Create a rule With Condition that Your TextBox Contains Value or not If Yes then Switch it to View 2 [ i.e Read Only].
If You have any queries Let me know