Problems with new SSD in Mid 2012 MBP

I have a mid 2012 MacBook Pro.

I wanted to swap the original HDD with a SSD. I bought the ADATA 480GB SSD [SU650].

I had created a bootable USB with a) Yosemite and b) Mojave. The USB sticks boot fine. When I tried to install the OS onto the SSD, the SSD did not even show up in the drive list. Tried the following:

1. Read that the SATA cable may be damaged while swapping. So, replaced the original drive (HDD) and checked it - it works fine.

2. It could have been the drive that is faulty: so, connected the drive as an external drive [USB - SATA cable]. The drive is recognized, and it has a GUID partition table.

3. It could have been some unknown issue, and some internet fora suggested that the current HDD can be cloned onto the SSD, and then the SSD can be directly used in lieu of a HDD. Failed again.

4. However, when I try to boot from the SSD as an external drive, it works fine.

Here is a list of what is fine:

1. HDD

2. SSD

3. SATA Cable

In summary: I am not able to get my MacBook Pro to recognize my SSD as my primary drive. I have not made any changes to the Optical bay. Any suggestions / solutions are most welcome.

Many thanks.

-WM

PS: at this point, I am very close to breaking my 10 yr relationship with Apple and go back to custom built Linux machines.