HOW DO I CORRECT THE CODE TO COPY CORRECTLY

Post all your code, and, ideally, a sample workbook.

hmmm...Set dstSheet = ThisWorkbook.Worksheets(1)

Right after this, try to see which sheet was picked up:

Msgbox dstSheet.Name

Also, it's good practice at the end to clear the objects:

Set R = Nothing

The MSGbox reads "dbSheet".
 

Sub CSM() ' Copies CSM data
Dim srcBook As Workbook
Dim srcSheet As Worksheet
Dim dstSheet As Worksheet
Dim R As Range
Dim foundRows(2) As Long, i As Long

'Application.EnableEvents = False
Application.ScreenUpdating = False
On Error GoTo crash


Set srcSheet = ThisWorkbook.Worksheets("CSM")
Set dstSheet = ThisWorkbook.Worksheets(1)
Set R = srcSheet.Range("B2")
 i = 0
  Set R = srcSheet.Range("B:B").Find(Right(dstSheet.Range("B15").Value, 5), R)
  If Not R Is Nothing Then
    foundRows(i) = R.Row
    If i = 0 Or Not foundRows(i) = foundRows(0) Then
    dstSheet.Cells(5 + i, 3).Value = srcSheet.Cells((foundRows(i)), 8)
    dstSheet.Cells(5 + i, 4).Value = srcSheet.Cells((foundRows(i)), 9)
    dstSheet.Cells(5 + i, 5).Value = srcSheet.Cells((foundRows(i)), 3)
    dstSheet.Cells(5 + i, 6).Value = srcSheet.Cells((foundRows(i)), 4)
    dstSheet.Cells(5 + i, 7).Value = srcSheet.Cells((foundRows(i)), 6)
    Else
      dstSheet.Range("C" & (5 + i) & ":H" & (12 + i)).ClearContents
      dstSheet.Range("C" & (5 + i)).Formula = "N/A"
    End If
  Else
    dstSheet.Range("C" & (5 + i) & ":H" & (12 + i)).ClearContents
    dstSheet.Range("C" & (5 + i)).Formula = "N/A"
    Set R = srcSheet.Range("B2")
  End If


'srcBook.Close (False)
'Application.EnableEvents = True
Application.ScreenUpdating = True
Exit Sub

crash:
Application.EnableEvents = True
Application.ScreenUpdating = True
MsgBox Err.Description
On Error GoTo 0
 
End Sub

Select allOpen in new window

First, a minor memory leak...replace this:

...
Exit Sub

crash:
Application.EnableEvents = True
Application.ScreenUpdating = True
MsgBox Err.Description
On Error GoTo 0
...


with this:

nocrash:

Exit Sub

crash:
Application.EnableEvents = True
Application.ScreenUpdating = True
MsgBox Err.Description
Resume nocrash


--
Confirm that dbSheet is the tab that has the data you want to read.

dbSheet is not any tab in theworkbok. there ar only 4 tabs.... one is CSM
SHEET(1)IS NAMED DIFFERENTLY ....BASED ON user name

Sorry about the workbook . It's all proprietary Client information
First the code works to the msg box
 Set R = srcSheet.Range("B:B").Find(Right(dstSheet.Range("B15").Value, 5), R)' picks up the correct value of R from cell B15
  If Not R Is Nothing Then ' the value  of R changes to the value of Range (B16")

    dstSheet.Cells(5 + i, 3).Value = srcSheet.Cells((foundRows(i)),8) " gete the correct value from source
    dstSheet.Cells(5 + i, 4).Value = srcSheet.Cells((foundRows(i)), 9)
    dstSheet.Cells(5 + i, 5).Value = srcSheet.Cells((foundRows(i)), 3)
    dstSheet.Cells(5 + i, 6).Value = srcSheet.Cells((foundRows(i)), 4)
    dstSheet.Cells(5 + i, 7).Value = srcSheet.Cells((foundRows(i)), 6)

Finally figured it out . There were 3 hidden worksheets on the workbook and the code was running against the hidden sheets-- dbsheet was a hidden sheet.
Once I delete the hidden sheets, everything worked

Excellent!  Glad you figured it out!