CharacterName_123456789 (The primary game state containing inventory, relationships, and farm layout)

You can copy PC save files directly to an Android or iOS device to continue your farm on the go, though this does not work in reverse for all versions. Backup & Share:

With (Stardew Modding API), you can install mods that fundamentally alter saving:

Follow the instructions in Section 1 to locate your Saves folder on the old PC. Copy the entire CharacterName_UniqueNumber folder.

The Myth of the PC Exclusive: Understanding Stardew Valley Save Data Transfer