Hello,
The transmissions may appear to be the same, both are 09G six speed automatic transmission.
They may bolt up and work fine, however I would be careful. Here is what I found and you can make your own decision to use a different transmission, personally, I would keep the codes the same because the KGL is the 'newer' one and maybe rated for more power? That is just an educated guess.
KGL (6A)
Part number: 09G300034B (09G300034BX)
For Engine codes: CBTA, CBUA and CCCA --> (125kW/170HP)
- Jetta 07/2007 to 12/2014
HRM (6A)
Part number: 09G300037M (09G300037MX)
For Engine codes: BGP, BGQ and BTK --> (110kW/150HP)
- Jetta 04/2005 to 07/2007
Hope this helps,
drpeter