What Android version & Device is he on ?
It is extremely important to know if the target device has a Firmware update coming soon and also it is important to know what Android Version the device is running on, both these pieces of information can be obtained by getting the target to load a website and provide data to the website for loading.
I made this page as an example of a browser user agent string reader Check Device & Browser example php
After you know the Android version is not going to change ( No Updates ) and you know what the Android Version is.. Then you can look into remotely monitoring that version of Android.
Let me explain some more,
On Android 4.4 or below,
You can track the text messages, calls, call history, message history, application launch history etc..
You can use several application's below Android 5.0 to monitor android almost invisibly.
My favourite would be the simple ones like SMS Forwarder and mainly any Parental Control apps, have a look around at the options, i haven't used Android 4.4 for age's so i can't even remember any others.
On Android 5.0+ Things get a lot, A Lot, Harder !
In Android 5.0 you need to select the SMS Handling application, this only allows 1 single application to Read the SMS Messages being sent !
However you can still receive SMS Message's easily using a Broadcast Receiver ( For Phone Number Verification in Applications )
So, on Android 5.0+ it will be very difficult without modifying the system of the phone to allow a monitor application.
Logs and LogCat Reading,
You can still read the sent message's using a Log reading method, It waits for the SMS to go into OutBox or Sent and then uses Read Messages permissions to list all message's in the default SMS App, once it has listed all the message's, it then checks by time to see was last sent.
However Android 6.0+ Implemented
( On Demand Permission Acceptance )
With Android 6.0+ you need to accept the permission to receive calls, sms sent & sms received information at each read... Their goes Invisibility...
Due to the massive number of permission changes to Android, it is probably going to be a fight to get an app working with all permissions permanently accepted so as to stay hidden.
You are the owner of both accounts
I have seen accounts being used to bypass the Messages & Calls & Contacts permissions by using Google Backup...
The Application initiates a Google Backup of everything on your device and then you can access that information by restoring it onto another device that you own.
Permission acceptance can stop monitoring software from working.
Default SMS Application Selection can stop SMS Sent monitoring.
Android 6.0 Stops Monitoring by using Permissions & SMS Application Selection.
Android 5.0 Stops Monitoring by using SMS Application Selection.
Android 4.4 or Below will not stop Monitoring at all.
OTA Updates can update your Android Version and bring about new problems as I've mentioned.
Both Devices Accounts are linked, so data can be accessible by Google Backup & Restore.
Some stuff can be monitored invisibly, however you need to accept the permissions permanently so the user never See's it.
Other methods than Malware or Spyware
A method sometimes used by Law Enforcement Agencies is to Clone the SIM Card, you can buy many SIM Cloning device's online and blank sim cards to clone into... However many ISP or MSP's are monitoring for Cloned sim cards and only allow 1 device to receive the message or call..
Sometimes it is at random who gets the text or call, but only 1 of them gets it.
SS7 is a security protocol that we all accept when using an Android device, as part of that we allow all our information to be accessible through the security protocol SS7... Even your Camera is accessible while your device is switched Off...
Many hackers have hacked SS7,
You can even use whole website bots that do the hacks Automatically by purchasing an account with them, software can also be purchased that hacks SS7 Automatically as well.
Root Access & Spyware
If the target has Root Access, thing's get a lot easier... Root Access Spyware can literally be invisible... You could manipulate the stock messaging application and also implant spyware into the system, i will not cover that here.
Ask him, tell him that you are unsure about his commitment to the relationship and you would just like to have some closure by looking through his phone ?
It is easy to delete a message and call history i know, but trust is a very powerful thing.