My research so far indicates that this is not easy to do if you want your solution to work on a wide range of models. For some phones, an App can do the trick, while for others, it simply won't work.
For the Sony Xperia series, for instance, there is not a single App capable of recording on a stock phone the internal speaker used for telephone communications. For this to be possible, this line of phones has to be rooted. The background is that the legislation of many countries forbid the unconsentious recording of phone conversations, which are regarded "private" there (rendering recordings of such communications usually inadmissible before a court of law). And Sony likes to be extremely cautious and tries to be politically correct, so as not to hurt sales in these countries.
For a similar reason, the unnerving shutter sound of the Sony Xperia series cannot be turned off unless the phone is rooted, not even in countries the legislation of which does not forbid the silent shooting of pictures of other people. Strangely, however, you can shoot a film without a shutter sound on these phones.
If you must record a call, as a workaround, you may turn the speaker on and use an App (or an library, if you want to develop yourself) that uses the microphone for recording.
Regards,
