letter could have a instance of base. In A would have a property that convert the instance of base to a.
Class letter
Inherits Forms
protected _base As base
End Class
Class A
Inherits letter
Public ReadOnly Property objA As a
Get
Return CType(_base, a)
End Get
End Property
Public Sub New()
_base = new a
End Sub
End Class
An other option is to create a user control that contains the similar functionality that would take a base as parameter. Then you just need to put that same user control into both forms.