I was thinking along the lines of a Worksheet_Change event such as:-
Private Sub Worksheet_Change(ByVal Target As Range)
Application.ScreenUpdating = False
If Target.Count > 1 Then Exit Sub
If Target.Value = vbNullString Then Exit Sub
If Intersect(Target, Columns("L:L")) Is Nothing Then Exit Sub
Target.EntireRow.Copy Sheets(Target.Value).Range("A" & Rows.Count).End(xlUp).(3)(2)
Application.CutCopyMode = False
Application.ScreenUpdating = True
This assumes that your criteria are in Column L so you would need to make your last entry in Column L of each row and as you click away (or press enter or down arrow) that row will be automatically transferred to the relevant sheet. You could also add a line to delete the "used" data from the Master sheet as you go if you would like (just remove the apostrophe at the beginning of line 12, the line in green font)
Another option would be to assign a code to a button and once you are done with the data entry, just click on the button to transfer the data to the relevant sheets.
Just some options for your future forays into VBA!
Again, thanks for sharing. Good luck!