I've done that before (Win10 to Mint18).
It's as simple as copying the threetwo wallet files (without extension, .address.txt<Wallet name>
, without extension and <Wallet name>.keys
) from Windows' Monero folder to Linux's Monero directory, start GUI/CLI wallet client on Linux, and enter your wallet password. The Linux executable is happy with wallet files generated by Windows executable. I believe the files will also work across architectures (x86/x64/ARM) but I have only tried x64 to x64.
As long as you still have access to your Windows partition (and the files therein), these steps should bring your wallet back with all funds intact. If your Windows partition is intact but you can't access it, consult your Linux distribution's documentation and/or head to Unix.SE.
If, however, your Windows partition is gone and you don't have the wallet files nor your mnemonic seed, your Monero are unfortunately lost. Take it as a lesson learnt and have proper backups in the future.