I have
You'll need to do the following:
... Or Can i build IPA file and share it with client, so he can submit to App Store?
To answer your question, you can build the app and provide to your client for them to submit the app.
For building the app (.ipa) you need to get the Provisioning profile & Certificate (.p12) corresponds to Apple developer program from the client.
I have done this for many of our clients and solution is working. In fact few of the clients they have an internal portal with the predefined process.
In case, if anyone of you have queries on this response comment below and I shall try to answer.
Note: when signing remember to choose use local signing assets in order to avoid giving apple id credentials.
As of Summer of 2017, Which is after this was initially asked) The developer and the app producer name must be the same. Thus just have them spend the $99 a year and get a Dev account that they add you to to Develop / manage.
Here is a short and detailed explanation: [1]: http://www.goodbarber.com/blog/your-client-s-developer-accounts-vs-your-own-a856/
Here is how to tranfer if already in app Store under your account:[1]: https://support.appmachine.com/hc/en-us/articles/360000012284-Transfer-your-app-to-another-iOS-Developer-Account
According to the description the simplest way would be to submit the app on your own behalf and as soon as you pass the certification to transfer the published app to your client from iTunes Connect dashboard.
For those who needs to do the same on behalf of clients, here are the steps i've followed...
What i had
What client had
As far as app distribution is concerned, apple have 2 systems: Member Center (for Certificates, Profiles, App IDs etc) and ITunes Connect (for publishing your app to app store and further management of the app).
I need access to both ITunes Connect & Member center for distributing on behalf of client.
This is what i did for submitting the app. If you find any mistakes/better alternatives, pls comment below, so i'll update the answer.
The easiest way would be to have your client add you under User and Roles in iTunes Connect. There is a developer role now that can limit access to a certain app and restricts it to the below: