If you would like your iPhone to remember the last song playback position, you need to configure your ITunes to remember the last song playback position.
To do so follow the steps below:
Open iTuens -> Music
Go to songs or artists or Albums you would like your iPhone to remember the playback position
Right Click on the object (song, songs, Artist, album or all Songs) and select Get info
Go to option tab and tick the box Remember playback position and click OK, to finish sync your iPhone and it should remember your last playback position.