linha is set to the last row but LR is the variable that is actually used for the last row.
linha = Worksheets("FAMINHO_ESCOLAS").Cell(Rows.Count, 1).End(xlUp).Row + 1
Cell( should be changes to Cells(.
linha = Worksheets("FAMINHO_ESCOLAS").Cells(Rows.Count, 1).End(xlUp).Row + 1
It would be better to qualify Rows.Count to the worksheet.
I prefer to write a separate sub routine to add the values. In this way, I can test the code without having to instantiate a userform.
Alternative Solution
Note: AddRowToFAMINHO_ESCOLAS will accept anywhere from 1 to 69 values.
Private Sub button_Click()
AddRowToFAMINHO_ESCOLAS boxname.Value, boxname.Value, boxinstr.Value, boxescola.Value, boxtel.Value, boxemail.Value
End Sub
Sub AddRowToFAMINHO_ESCOLAS(ParamArray Args() As Variant)
With Worksheets("FAMINHO_ESCOLAS")
.Cells(.Rows.Count, 1).End(xlUp).Offset(1).Resize(1, UBound(Args) + 1).Value = Args
End With
End Sub
AddRowToFAMINHO_ESCOLAS Demo

Addendum
This function will return the last row with values in column A.
Function GetFAMINHO_ESCOLASLastRow() As Range
Dim Target As Range
With Worksheets("FAMINHO_ESCOLAS")
Set Target = .Cells(.Rows.Count, 1).End(xlUp)
Set Target = Intersect(Target.EntireRow, Target.CurrentRegion)
End With
Set GetFAMINHO_ESCOLASLastRow = Target
End Function
You can test this function by entering the following code into the Immediate Window:
Application.Goto GetFAMINHO_ESCOLASLastRow
Response to Question Update
I changed things up a bit because the OP wants to write and retrieve the values.
Private Sub buttonleft_Click()
Dim Target As Range
Set Target = GetFAMINHO_ESCOLASLastRow
With Target
boxname.Value = .Cells(1, 1).Value
boxinstr.Value = .Cells(1, 2).Value
boxescola.Value = .Cells(1, 3).Value
boxtel.Value = .Cells(1, 4).Value
boxemail.Value = .Cells(1, 5).Value
End With
End Sub
Private Sub buttonright_Click()
Dim Target As Range
Set Target = GetFAMINHO_ESCOLASNewRow
With Target
.Cells(1, 1).Value = boxname.Value
.Cells(1, 2).Value = boxinstr.Value
.Cells(1, 3).Value = boxescola.Value
.Cells(1, 4).Value = boxtel.Value
.Cells(1, 5).Value = boxemail.Value
End With
End Sub
Function GetFAMINHO_ESCOLASLastRow() As Range
Dim Target As Range
With Worksheets("FAMINHO_ESCOLAS")
Set Target = .Cells(.Rows.Count, 1).End(xlUp)
Set Target = Intersect(Target.EntireRow, Target.CurrentRegion)
End With
Set GetFAMINHO_ESCOLASLastRow = Target
End Function
Function GetFAMINHO_ESCOLASNewRow() As Range
Set GetFAMINHO_ESCOLASNewRow = GetFAMINHO_ESCOLASLastRow.Offset(1)
End Function