* Transmission Type: The exact transmission type (e.g., 46RH, 47RE, 545RFE) needs to be identical or at least very closely compatible. Even a slight difference in the transmission model can mean incompatible bolt patterns, input/output shaft lengths, and electronic controls.
* Bolt Patterns: The transmission's bellhousing bolt pattern must match the engine. These changed over the years.
* Electronic Controls: The 2003 transmission likely uses a more advanced electronic control system than the 1999 model. This might require significant wiring modifications, potentially including a new transmission control module (TCM) and harness, which is a very complex undertaking.
* Torque Converter: The torque converter is crucial and must be compatible with both the transmission and the engine.
In short, while some parts *might* be interchangeable, a complete swap is a major undertaking that requires expert knowledge and likely significant modifications. It's much more likely to be easier and cheaper to find a used transmission specifically for a 1999 Dodge 1500. Trying to adapt a 2003 transmission could lead to considerable frustration and expense.