The license of the typeface, along with other tools you need for design work, should be bought by the designer herself/himself. The client will buy a finished product and is not supposed to work on the typeface himself. The advantage here is that designers can use the same font on multiple projects.   If the client wants a copy of the typeface files, then the license must be bought in his name. In this case, you won’t be allowed to use the font after the completion of this client’s project or on any other projects you are working on.