It's a bit unclear whether transporting matter "as is" is the more difficult feat, or altering of the details of matter.
I mean, the former would seemingly require knowing the matter down to the absolute finest detail - but the transporter could well "cheat", moving the matter in "lumps" that already contain a lot of information. It's not as if an automobile needs to understand quantum physics and scan the passengers down to quantum level in order to get them from A to B at "perfect resolution".
In contrast, creating modifications at resolution X would seem to require resolution X or better in all circumstances. Even if one introducted the modified matter in a "lump", making it fit in the intended place would seem to call for resolution X at the edges...
Thus, the A-to-B transporter might be invented significantly earlier than the device that can manipulate matter, biofilter it, turn yeast into turkeys and so forth.