Q:

Can we migrate users with their questions?

If a question is migrated from MO to MSE, would (or should) it be possible to automatically create the user an account at MSE and link it to the one at MO if they don't have an MSE account yet?
I don't know if users in this situation get an automatic suggestion to make an account at MSE, but at least it's not created automatically.
(They do get a notification about migration. See quid's answer.)
New users may be puzzled about how different sites and accounts and migration and not really know what happened.
A bigger problem is that the migrated question does not have an owner at MSE, and comments and questions don't reach the OP, and the OP is not there to accept and enjoy the answers or improve their question.
I imagine that migration without the OP having an account at the target site makes the question more likely to be abandoned.
Fortunately users do get notifications of their migrated posts even without an account on the target site.
Copying an account to a different SE site automatically might be too much, but it should at least be automatically recommended to the user.
I'm not sure if copying the account really is too much, though; we do migrate questions without asking the OP and one could think of a single SE account expanding to new SE sites within the same system.
The user can of course delete or merge their new account if they are not happy with it.
It should probably be noted that this question is not really about making the life of active MO users easier, but about helping new users find the right place for their questions and also answers to them.
Edit:
I find automatic account creation a bit extreme (and confusing) myself, too, although I don't think it would be completely out of question.
I think that in a case of migration the user should get a strong suggestion to create a new account.
(Or maybe I should just try to feel less sad about some questions ending up abandoned because they were originally asked in the wrong place.)

A:

Users get a notification of migration in their inbox. If/when they create an account on target site, they get the migrated question attached automatically.  
While I agree migration can be confusing, I think that on the one hand creating an account on another site, even if it is in the network, is perhaps a bit too invasive (the migration is already somewhat invasive), and on the other hand it will not help that much to ease the confusion (account-creation, especially if one has one in the network already, is pretty direct).    

