SSD cannot be seen, but other mac sees it when in target disk mode

I have a late 2013 macbook pro 13" A1502 ("A"). Recently the computer would not boot, so i wiped the hard drive via target disk mode via thunderbolt with my 2011 macbook pro 17" ("B") and installed the operating system. Laptop A worked fine with High Sierra. However, my father kept complaining how slow it was now. I wiped again in target disk mode and attempted to install mavericks with no luck (got prohibitory sign on boot after i installed).

I guess there is obviously a problem with the 13" logic board, however the thunderbolt connection is able to detect the SSD. My question is: Is it possible to successfully image the 13" from the 17" while the 13" is in target disk mode?"