The world is only saved on the person's computer which is hosting the server - so not on your machine.
You could ask your friend to send you the world files - usually located at "C:\Users\<username>\AppData\LocalLow\IronGate\Valheim\worlds" - and copy that into your worlds-directory. (unless it's a dedicated server, then the world files may be somewhere else - dunno, my dedicated servers run on linux)

This has one downside - the world on the server and your local one will not be synced in any way, so progress on one world will not affect the other ... an maybe the client won't be able to tell the difference between the local and the remote world, so your map might be a little confused (at least this happens if you create, delete, recreate ... the same world with same seed over and over again)