试试这个（我不能测试它，只是一个想法）

'Somewehere declare this string variable
Dim incomingHTMLBody as string

olItems.Sort "ReceivedTime", True
For i = 1 To olItems.Count
    Set olMail = olItems(i)
    If InStr(olMail.Subject, "Desired_Subject " & TheDate) > 0 Then
        incomingHTMLBody = olMail.HTMLBody
        Set olReply = olMail.ReplyAll
        With olReply
            .Display
            .To = "Recipients@gmail.com"
            .CC = ""
            .Subject = "Test_Subject"
            '.Attachments.Add "Document_destination"
            .BodyFormat = olFormatHTML
            .HTMLBody = "This is a test email sending in Excel" & incomingHTMLBody
            Exit Sub
        End With
    End If
Next i
End Sub

在环境中引用Outlook对象时可能需要多加小心。

Option Explicit ' Consider this mandatory
' Tools | Options | Editor tab
' Require Variable Declaration
' If desperate declare as Variant

Sub Find_Email()

Dim objApp As Outlook.Application
Set objApp = CreateObject("outlook.application")

Dim objNS As Namespace
Set objNS = objApp.GetNamespace("MAPI")

Dim objMailbox As Outlook.Folder
Set objMailbox = objNS.Folders("Group_Inbox")

Dim objFolder As Outlook.Folder
Set objFolder = objMailbox.Folders("test_Folder")

Dim subFolder As Outlook.Folder
Set subFolder = objFolder.Folders("test_subFolder")

Dim objItems As Outlook.Items
Set objItems = subFolder.Items

Dim TheDate As Date
TheDate = Format(Date, "DD-MM-YYYY")

'Find most recent email and populate

objItems.Sort "ReceivedTime", True

Dim i As Long

Dim objMail As Outlook.MailItem     ' olMail is not a good variable name
Dim objReply As Outlook.MailItem

Debug.Print objItems.Count

For i = 1 To objItems.Count

    Debug.Print objItems(i).Subject
    
    If objItems(i).Class = olMail Then   ' verify item is a mailitem
    
        Set objMail = objItems(i)
        
        If InStr(objMail.Subject, "Desired_Subject " & TheDate) > 0 Then

            Set objReply = objMail.ReplyAll
            With objReply
                .Display
                .To = "Recipients@gmail.com"
                .CC = ""
                .Subject = "Test_Subject"
                '.Attachments.Add "Document_destination"
                .BodyFormat = olFormatHTML
                
                Debug.Print .htmlbody   ' verify property is available
                
                .htmlbody = "This is a test email sending in Excel" & .htmlbody ' This is the problem line.
                
                Exit For
            End With
        End If
        
    End If
    
Next i

End Sub