Short answer is No you can not. Thus either check the Nokia Store whether the app is still available, or contact the original developer for assistance.
And here's the longer answer:
Basically, if the application is installed into memory card, you could of course find & extract all files from there. But if you simply move to them to other device, they would not work, since the internal drive is not having the check sum etc. files required by the platform security.
Then to get the security stuff work ok, you would need to have the installation file for the app. In theory you could simply make the pkg file and use the files you can extract from the device, and use makesis to create the installation file. And then use signsis to sign it with your own self-made certificate.
This would then only work, if the application only uses capabilities allowing self-signing.