To copy contacts and messages between two phones we recommend to have the Phone Copier app installed on both, but it is absolutely necessary to have it installed on the destination device (the one you want to transfer the data into).
When you want to transfer the data, please turn Bluetooth ON on both devices - as that is the quickiest way to do it. Then inside the Phone Copier app select "Bluetooth Import" on the destination device.
Let both phones discover each other, and pair them (you will see a popup message asking for pairing approval). Once done, select what data you want to transfer and tap on OK.
The reading operation should be initialized by then and the data should be transferred.
Please note that while transferring messages, you might be asked by the Phone Copier app to be set as "default messaging app" for your phone, which we kindly ask you to allow, due to the restrictions of Android 4.4 and higher. After the copying is done, the app should ask you itself to revert the process and set the Messaging app as a default again.
If you do not receive the prompt to select a default messaging app, then you can find the option to manually select the default messaging app in your phone settings, in "General or Apps".