Generator to top off batteries

Hi guys, I need some advise and I am just going to apologize if this is a 💩question 🙂. I have 2 x Growatt SPF5000ES inverters hooked up to 2x LBSA Lifepo4 batteries. From time to time in my area we go down for days on end and on cloudy days, my panels just cannot get my batteries charged fast enough in order to run my things in my home. Question here then is: Could I use my generator to top up my batteries by hooking up an adequate Lifepo battery charger to the generator and connecting the charger directly to the master battery pack? Or would you recommend an additional change over switch at the AC in to the inverters and connecting the generator to the gen input thus feeding the inverter directly from the generator? (I guess the latter option might cause issues as my genny is only 6.5kva and if the inverter is directly fed, depending on my source mode it might want to power the house and charge the batteries at the same time...) too many amps I guess. 

Anyway, I hope you get what I am after and I am hoping someone here could give me a piece of good advise. 

Thanks