The F135 is larger in diameter, length, and weight than the F119, and would never fit in the F-22 engine bay.
The core module of the F135 is a development of the F119 core with some more advanced technology incorporated. There was a study done on what it would take to install the F135 core into the F119 to take advantage of the technology advancements and bring some commonality to the Depot overhaul process. It was decided at the time that this change was not worth the cost of implementation.
With the F135 Engine Core Upgrade in development, it seems like the ECU could also be incorporated into the F119 with similar changes that were identified in the previous study. Whether it would be cost effective or bring enough performance increase within the remaining F-22 life span is doubtful.