Your new SSD is installed inside an external enclosure, correct? And you successfully completed the installation of OS 10.12.3 onto that SSD (or a partition on it), correct? Finally, you did not "migrate"/copy any "stuff" from anywhere else (like from the 13" MacBook Pro), correct?
Assuming all of that is accurate, that 850 EVO SSD is now just like having another computer, as you have a bootable OS (ie, Sierra) on it. Given that it is just the OS (and Apple "supplied" software), it's basically like buying a new Mac that already has the OS on it. You then need to go through the normal setup process of a new machine.
I have gone through a similar process before, but after the installation of the OS, I "migrated"/copied stuff from a SuperDuper! backup to that partition, and that copying contained OS "setup" information like my admin account, password, etc.
In your situation, at this point, you should be able to disconnect everything, remove the 850 EVO SDD from the external case, remove the old drive from the 2011 MacBook Pro, install the 850 EVO SSD inside the 2011 MacBook Pro, close up that machine, and boot it up. That should be just like getting a new Mac, and you then will need to go through all the "new" setup steps, like setting up an admin account/user, password for that account/user, date, time, etc.
I guess the other thing you could do is to try this: with the SSD connected to the 13" MacBook Pro, boot up the MacBook Pro. You should subsequently see the partition/partitions for the 850 EVO SSD on the MacBook Pro's desktop. Go to System Preferences, and select Startup Disk. You should see at least two disks there to choose from: the startup disk for the MacBook Pro (ie, its internal drive), and the OS 10.12.3 partition disk on the 850 EVO SSD. Select the 850 EVO one, click on Restart, and what will basically happen is that you are booting from that 850 EVO partition, but using the MacBook Pro's screen to work. If you are first asked to enter a password, I suspect that would be the one for the MacBook Pro. After that, you should be able to go through the entire setup process for OS 10.12.3, including setting up your account, password, time zone, date, etc. Again, though, I have never actually gone through such a process, but logically, it should work.