You can create a draw.io diagram in a specific Google Drive folder by selecting that folder in the Drive interface,

 

 

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pressing the new button, then select "More...",

 

 

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then select draw.io Pro.

 

 

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The new diagram will be created in that folder.

You can move existing diagrams either in the Drive interface by right clicking the diagram and selecting "Move to...:

 

 

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Then selecting the destination folder.

Or, within draw.io, select File->Move To Folder:

 

 

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and then select the destination folder.