Case Swap?

the short answer is yes, it can be moved. Only difficulty is re-using your CPU kooler, you'll want to replace it with something like Corsair H80i V2, any type of kooler that allows just the pump to plug into the motherboard CPU fan header, and the pump then relays power to the radiator fan(s) over dedicated fan wiring connectors, see photo

Due to a shortage of fan headers on the R4 motherboard + the 'special' 7pin power connector end of the stock kooler you have now, to transfer it to a new case would involve moving the MIO AlienFx daughterboard + the top light strip to get it all back to working which may be impractical

PlanB

Buy something like this to power the cooling pump > https://www.ebay.com/itm/3-Pin-to-4-Pin-Fan-Power-Adapter-Cable-Pass-Through-NEW/391472732921?hash=item5b2597daf9:g:LWAAAOSw-olZ5XtW

Next, buy a different radiator fan, a 4pin PWM type rated at 1AMP or less (the server-grade 38mm wide Delta or Nidec radiator fan you have now is ~1.5AMPS, where the rule-of-thumb for older boards is not to exceed 1AMP of draw off of a fan header which the stock 1.5AMP fan will do > note that it is already isolated from motherboard on its own dedicated circuitry to deliver the 1.5AMP call when it wants it). A 25mm wide Corsair SP120 or MagLev 120, Noctua, any 4pin PWM fan with a good static pressure rating / high CFMs would be ok. CoolJag 32mm wide is ok, rated at 1AMP. To re-use your current Delta Nidec fan against advice is on you ( http://www.frozencpu.com/products/15476/fan-965/Cooljag_Everflow_120mm_x_32mm_PWM_Fan_R1232BUAF.html )

PlanC (see also CPU Pump power needs)

Cut the 7pin end off of the pump, make the ribbon cable into a basic 3-wire (no need for the 'ground jumper' anymore, break or cut it off), crimp your own fan pins onto the end and insert them into an empty 3pin fan connector & plug that into a Molex-to-fan adapter (as seen earlier) so it gets constant 12volts / ground. A shielded 3pin connector would then be ok also (seen below)

PlanC Supplies

• http://www.frozencpu.com/products/1821/ele-173/3-Pin_Power_Supply_Connector_Pins_Set.html?tl=g51c393s2092
• http://www.frozencpu.com/products/1840/ele-191/FrozenCPU_3-pin_Male_Fan_Connector_-_Black.html?tl=g51c389s997 

• https://www.ebay.com/itm/3-Pin-to-4-Pin-Fan-Power-Adapter-Cable-Shrouded-FREE-S-H/371746512990?hash=item568dd1a05e:m:mg8F8lTuJvKNIRG8wWOvQ1w 

Front Panel Wiring

Your custom MSI motherboard will have the above 'front panel header' pinout; compare it against the micro-text on your actual header, it is the yellow-rainbow header bottom-right of sill. Hook your new case wiring (Pwr On / Pwr On LED / HDD LED / RESET) there (see your new owner manual. The form factor (size) of this board is a micro-ATX 9.6 x 9.6 and requires a case suited for m-ATX / u-ATX boards

That's what I think about your question, you can of course wait for other member input

Best advice: get the un-shielded adapter (Molex 4pin to 3pin fan), get a different radiator fan to plug into the very top right CPU_Fan header

If you get bored, I offered about the same advice on moving Area-51 motherboard / cpu kooler into an aftermarket case, here

Area 51 ALX motherboard and cooler. HELP!!

comparing 7pin to 3pin 'fan' type pump connectors