Yes you can mix up the batteries in series but keeping in mind that is not recommended to mix different capacity batteries or different ages or differently treated batteries.
But as APC is also not made to power the station pump or ceiling fans but we are using them like that way so Pakistan zindabad
Some advice or tips .
I know it's an old thread and you have already bought the battery.
It is good to charge Both the batteries at fullest first and then leave them for 24 hours without Connecting with anything .
After 24 hours check the specific gravity from an inexpensive gadget named the hydroMeter , if the difference is more than 0.3 between different cells then balance them by adding or removing electrolyte to / from cell and pour into another Cell until you will see all the cells gravity is equals. Now you can connect them in your APC and use but the game is still remaining, once these batteries will be discharged and the APC shuts Off then again you need to check the specific gravity of all cells and again balance them. And then put them on charge.
If you have a solar charger then the above method will not work well because of some technicalities. But if you are using KESC or wapda ETC then it will work.
Have tested this method already.
Do update the results as it will be a hand on experience.
Sharing is everything.