You can place your custom title templates on a shared server, but your individual users will need to install it on their individual systems in order for them to work. And it's not a simple file. It's a whole folder.
You don't say what operating system you're using but on Windows 10 your custom motion title templates are located in C:/Windows/Users/[UserName]/AppData/Roaming/Adobe/Premiere Elements/15.0/Rich Title Templates/Custom. (You will likely need to turn on Show All Files in order to see this directory.)
Your custom motion title will show up as a folder in which are about 60 files. This entire folder is your custom motion title.
I can't guarantee that copying this folder to another computer will mean that Premiere Elements will recognize and will add it to the user's custom templates -- but, if it does work, this is the only way it will.
Please let us know if it works.
I have the same issue, the only difference is that I'm trying to transfer between Mac machines.
Then the same answer applies.