Try:
Dim xlWkSht As worksheet, wdObj As Object, wdDoc As Object, fname As String
fname = "test"
Set xlWkSht = Sheets("sheet_name")
Set wdObj = CreateObject("Word.Application")
With wdObj
.Visible = False
Set wdDoc = .Documents.Open(FileName:="C:\path\" & fname & ".doc")
With wdDoc
.InlineShapes(1).OLEFormat.Object.Text = xlWkSht.Range("A2").Value
.InlineShapes(2).OLEFormat.Object.Text = xlWkSht.Range("A3").Value
.SaveAs FileName:="C:\path2" & fname & ".doc"
.Close
End With
.Quit
End With
Set wdDoc = Nothing: Set wdObj = Nothing: Set xlWkSht = Nothing
Note: The above code assumes your ActiveX controls are the first two in the Word document. If not you'll need to adjust the numbering or, if their relative location in the document varies, implement a loop to find them via their OLEFormat object names (e.g. "TextBox1", "TextBox2"). Note too that there is no need to change folders for the save: simply tell Word where to save as part of the Save expression itself.
On a side note, if you're after textboxes that are easily moved around, I'd have opted for standard Word textboxes or, perhaps, content controls (docx format). Otherwise, I'd eschew all types of textbox/control and simply write to bookmarks.