In behaviors you always need to use "of me" to refer to the child controls. This is particularly important in a data grid where there's lots of groups with fields called Line
So try:
put fld "Line" of me into fld "fullLine" of cd "full_Line"
go cd "full_Line"
I just re-read and you said the script is on the line field itself so:
put the text of me into fld "fullLine" of cd "full_Line"