Installing this application onto your SD card will cause some unexpected behaviour.
The app will function while installed on your SD card, but your experience will not be the same as when Enhanced SMS & Caller ID is installed on internal memory.
First off, the widget will disappear when you shut off your phone. This is something that Android does and we have no control over.
Second, the boot on phone restart feature of Enhanced SMS & Caller ID will not work. Again, this is because the system notification that Android sends out to third party applications occurs before applications installed on the SD card are made available to the system [1].
Thirdly, Enhanced SMS & Caller ID cannot ensure that it is always on (except when you shut it down via Enhanced SMS & Caller ID's menu) if you install this application to your SD card. Again, this limitation exists because Android prevents applications from using the system alarm [1].
Finally, your settings may not be reflected right away. We have found that some users have had to restart Enhanced SMS & Caller ID in order to have their settings reflected in the operation of the application [1].
If you can live with these limitations, then please go ahead and move the app to the SD card.
Some users have mentioned that moving the application to SD card using Link2SD, overcomes these limitations.