I've been through the ringer and back trying to figure this out. The download stops at around 1045-1050mb of 15078 and gives the " Unable to download patch files [20512],[25008],[20495]" which I assume is the last part of this process. I've called SE, Sony (NOTE: Sony can't help with this) and Charter (my ISP) several times in the past few days to find a solution and I've come up empty handed. I just received my new ps4 and was doing a simple ps3 to ps4 transfer on Nov 29 this year when I came across this issue. I've also tried a couple of steps that were explained in these forums in which I had no success therefore I will explain the steps I've taken to look into this and perhaps someone else will have better luck.
Anyway, after many phone calls between several companies I decided to send SE an email explaining this instead of calling them back. They responded and gave me a list of things to try. The first thing was to make sure that in your PSN internet browser that you have cookies and java enabled (When the browser is open simply click options on the controller and click the settings at the top on the right). I erased the cookies and websites if any, deleted any trace of FFIV and reinstalled ARR and HW & I had the same issue.
Second, I was told to check my date and time settings on the PS4 and not to do it manually, but allow it to change the time via the internet. Then shut the system down and reboot. Same thing occurred. Third they said to disable/shut off anything that uses your router/modem to prevent interference. This didn't help and I also made a direct connection to the PS4 with my modem and still nothing.
Fourth I was told to check the Port Ranges on my router/modem to ensure that the ports have been opened/forwarded/triggered. These were UDP - 55296,55551 & TCP - 80,8080,443,55296,55551. I called my ISP ( Charter Communications) and asked them about these ports and it seems that Charter has ports 80, 8080 closed to inbound traffic and allows outbound traffic only. All of their equipment is setup the same and they cannot open these on their end. Therefore I called my router company and was told to go into my routers setup page and in admin settings I turned on port 8080 & opened it. I confirmed the port was open by using yougetsignal.com. Then I port forwarded my router to only run to the PS4 with a static IP I created. I also added 3 separate inbound traffic rules to my firewall allowing port access from ports 80,880,443. This didn't solve it either. Apparently my router company told me they cant open the ports in general but this allows it to be used by bypassing the modems block on the inbound traffic. Only the ISP can actually open it from what they said.
Since my ISP cant or won't open these ports ( from what they said it is to prevent people from establishing web domains etc through their basic service... whatever) I can't think of anything else to do. I would assume that SE could create a patch that doesn't prioritize those specific ports or something that can help us connect to the servers to at least get by this one small part that prevents it from continueing. There's obviously some interference between Square Enix's servers and the PS4 during the data transfer to the ps4.
With that said...Square Enix please help with this issue, because we are paying you to play a game that has been and will remain dormant until this is resolved. Thank you. Anyway, good luck to you all and if you find anything else out please post and i'll do the same.