To move your #Matrix account from one instance to another without losing your current chat history do as follows:

0.5) Create a backup phrase
1) Use the Element desktop client with your existing account to in Settings - Encryption - Export your keys.
2) Create your new user account and use the Element desktop app to import the keys you just exported.
3) With your old account, invite the new account to all rooms you're in (including 1on1 chats). Make sure the room setting is correct for "Newly joined users can see history".
4) With your new account, accept all invites.
5) With your old account, leave all rooms.

Done.