Hi. Thanks a lot for your support Jerryzy, sorry for the delay but ...
So... After many many tests, here are my conclusions :
- GetFileByServerRelativePath , GetFileByServerRelativeUrl, GetFolderByServerRelativeUrl ... do not work as soon as it is performed in another site collection (same as SPMoveCopyUtil). So I could not use your example, and then...
- I tried to use SPServices, I failed
- At last I used SP.FileCreationInformation using the same technique as in your example (loading the file in memory and then creating the file at the destination) and finally ... it run!!! ...
- until a big file had to be copied, I had to change the server limits for API size limit (https://sharepoint.stackexchange.com/questions/111573/sharepoint-2013-javascript-code-for-file-upload-max-limit-exceeded/157307)
I am happy it runs nows, but I am really disappointed when I think about all the time spent. Javascript + API bugs -> lot of pain :-)