This code autofilters the rows on the activesheet where J =0, copies them to the first blank row on the second worksheet, then deletes the rows from the activesheet.
Change this line Set ws2 = Sheets(2)
to copy the rows to a different sheet, ie Set ws2 = Sheets("Your Sheet Name")
or Set ws2 = Sheets(5)
for the fifth sheet etc
Sub MoveEm()
Dim ws1 As Worksheet
Dim ws2 As Worksheet
Set ws1 = ActiveSheet
Set ws2 = Sheets(2)
Dim rng1 As Range
Application.ScreenUpdating = False
With ws1
.AutoFilterMode = False
.Columns("j").AutoFilter Field:=1, Criteria1:="0"
With .AutoFilter.Range.Offset(1, 0).EntireRow
Set rng1 = ws2.Cells.Find("*", ws2.[a1], xlValues, , xlRows, xlPrevious)
If rng1 Is Nothing Then
Set rng1 = ws2.[a1]
Else
Set rng1 = ws2.Cells(rng1.Row + 1, "A")
End If
.Copy rng1
.Delete
End With
.AutoFilterMode = False
End With
Application.ScreenUpdating = True
End Sub