On the origin Galaxy server:
Click on the name of the dataset to expand the info.
Click on the Copy link icon galaxy-link.
On the destination Galaxy server:
Click on Upload data > Paste / Fetch Data and paste the link. Select attributes, such as genome assembly, if required. Hit the Start button.
Note: The copy link icon galaxy-link cannot be used to move HTML datasets (but this can be downloaded using the download button galaxy-save) and SQLite datasets.