After replacing battery, laptop shuts down without warning

Thanks for your help and sorry for the delay in responding – thanksgiving has kept me from handling my tech issues :)

So here's the longer story. When I bought the computer in 2013, I replaced the superdrive with an extra HDD for storage. Both it and the solid state drive I use as my boot drive were getting up there in years, so I replaced them a few weeks ago. In so doing, I did a clean install, upgrading from Sierra to Mojave.

Upon installing Mojave, I noticed an immediate decrease in battery life to around 2 hours on a full charge (from around 5). I inspected the system profiler, did some research, and discovered that my battery had gone past the recommended cycle count and was due for an upgrade. I bought the ifixit battery kit and replaced it. As soon as I did this, the issues with instant shut downs began.

Per your suggestion, I reinstalled the old battery and charged it for a few hours. There have been no issues with unexpected shutdowns. I will post the coconut battery results below.

You know the saying, "If it ain't broke, don't fix it". That old battery looks just fine. What I am worried about is the Mojave installation and how it was done as it can cause real problems with trying to impose APFS formatting on existing third party SSD and SSHD drives, when installed as an upgrade to an existing system.

The old battery is working okay in terms of no shut downs, but as I mentioned, the battery life has been cut down to <2 hours of regular use on a full charge, which is less than ideal.

The drive is a samsung 860 evo. I had been successfully running many other versions of osx off my old third party solid state hard drive. Here was my (probably unnecessarily complex) mojave installation process. But I had troubles with downloading the osx installer, and it was the way I got it to work.

I pulled the old HDD (used entirely for storage) and replaced with my new HDD. I created a small partition on that drive, and installed Mojave on it. Then I shut down, pulled the old SSD, and replaced it with the new SSD. I booted from the bootable partition on the HDD, used disc utility to format the SSD as MacOS extended (journaled), then installed Mojave on the SSD.

Thanks again!

Any thoughts on the installation? Do you think that's to blame for the battery decrease? Should I just return the battery as defective given the lack of shutdowns on the old battery?

see update to answer