The Code from your attachement:
Sub FORIFIF()
Dim CHECKROW As Long
Dim INVENTROW As Long
Dim OUTPUTROW As Long
        
Application.ScreenUpdating = False

OUTPUTROW = 1

    For CHECKROW = Sheets("Prüfliste").Range("A" & Rows.Count).End(3)(1).Row To 2 Step -1
        OUTPUTROW = OUTPUTROW + 1
        Sheets("Ausgabe").Cells(OUTPUTROW, 1).Value = Sheets("Prüfliste").Cells(CHECKROW, 1).Value
        Sheets("Ausgabe").Cells(OUTPUTROW, 2).Value = Format(Now, "DD.MM.YYYY HH:MM")
        Sheets("Ausgabe").Cells(OUTPUTROW, 3).Value = "bydo@vba.ms"
        Sheets("Ausgabe").Cells(OUTPUTROW, 4).Value = "bydo"
            For INVENTROW = Sheets("Inventar").Range("A" & Rows.Count).End(3)(1).Row To 2 Step -1
                If Sheets("Inventar").Cells(INVENTROW, 3).Value = Sheets("Prüfliste").Cells(CHECKROW, 2).Value Then
                    If Sheets("Inventar").Cells(INVENTROW, 6).Value = "aktiv" Or Sheets("Inventar").Cells(INVENTROW, 6).Value = "wartend" Then
                        Exit For
                    Else
                        Sheets("Ausgabe").Cells(OUTPUTROW, 5).Value = Sheets("Inventar").Cells(INVENTROW, 2).Value
                        Sheets("Ausgabe").Cells(OUTPUTROW, 6).Value = Sheets("Inventar").Cells(INVENTROW, 5).Value
                        Sheets("Ausgabe").Cells(OUTPUTROW, 7).Value = Sheets("Inventar").Cells(INVENTROW, 6).Value
                        Exit For
                    End If
                End If
                If Sheets("Inventar").Cells(INVENTROW, 4).Value = Sheets("Prüfliste").Cells(CHECKROW, 2).Value Then
                    If Sheets("Inventar").Cells(INVENTROW, 6).Value = "aktiv" Or Sheets("Inventar").Cells(INVENTROW, 6).Value = "wartend" Then
                        Exit For
                    Else
                        Sheets("Ausgabe").Cells(OUTPUTROW, 5).Value = Sheets("Inventar").Cells(INVENTROW, 2).Value
                        Sheets("Ausgabe").Cells(OUTPUTROW, 6).Value = Sheets("Inventar").Cells(INVENTROW, 5).Value
                        Sheets("Ausgabe").Cells(OUTPUTROW, 7).Value = Sheets("Inventar").Cells(INVENTROW, 6).Value
                        Exit For
                    End If
                End If
                If INVENTROW = 2 Then
                        Sheets("Ausgabe").Cells(OUTPUTROW, 5).Value = "nicht gefunden"
                        Sheets("Ausgabe").Cells(OUTPUTROW, 6).Value = "nicht gefunden"
                        Sheets("Ausgabe").Cells(OUTPUTROW, 7).Value = "nicht gefunden"
                End If
            Next INVENTROW
    Next CHECKROW
    
    Application.ScreenUpdating = True
    
End Sub
I think we can make that 5500 times faster