* two Dell 27" monitors - both with max resolution of 2560. Dell U2715H and Dell U2713HM
* AMD Radeon R7 240
* video driver: Provider: Advanced Micro Devices, Inc. Date: 11/25/2015 Version: 15.201.2401.1001 Digital signer: Microsoft Windows Hardware Compatibility Publisher
* Windows 7 64Bit
one of monitors shows its native 2500 resolution (connected to HDMI) - all good,
but the 2nd one (connected to DVI) only shows 1920 instead of its native 2560. the resolution selection for this monitor shows this 1920 as its max ("recommended")
is this a fundamental limitation of AMD Radeon R7 240? can it show 2560 on both monitors?
There are dual link DVI models of that card but most likely yours is only single link. Max on a single link DVI is 1920 x 1200. So you would need to use a different connection method or a card that has dual link DVI.
It is upto the card manufacturer what connection methods they install on the boards.