Using a 120 volt inverter to apply 120 volts to a generator won't work. Using a motor to drive a generator to put 120 volts into the output of a 120 volt inverter won't work.
Every time you go through a power conversion, there is a loss due to the efficiency of the conversion. No conversion process is 100% efficient (although a few come rather close; better than 99%)
What you have there is a fairly complex way to drain a battery more quickly than if you left out most everything.
This is the third in a series of circuits involving numbers of motors, generators, and batteries. At a guess, they are supposed to be not only perpetual motion devices, but are also supposed to produce an excess of power.
Why the OP persists in this pursuit, or where some of these creations come from is a bit of a mystery.
To me going for overunity is like drawing a pentagram and making gold materialize. It is the same thing. Why? Because energy and matter are the same thing. If you can't make a thing like a gold coin from nothing why should you make energy from nothing. These are natural laws, which work well, as opposed to magic, which doesn't.
I copied the majority of this post from thatoneguy's blog and couldn't help myself. I can't help wondering why the true believers don't understand they are believers in magic. Might as well wish for a magic amulate, it makes as much sense. You do not create matter (which is also the same as energy) from nothing.
An interesting result comes from entering "recycling generator + perpetual motion" as a search term. I am happy to see our refutation of such things appear. The interesting part is in following the mostly magnetic perpetual motion device links.
The article that comes up singes the praises, but is not primarily interested in your funding "research", as so many of the sites do. However, click a link from that page, and it's right down the rabbit hole. It seems that magnetic generators have been common for years, and the power companies all use them. Their electricity is all free (one has to suppose burning coal in huge quantity is only done as a cover). As you look in almost stunned wonderment at these assertions, a popup box appears asking if you want to talk to a virtual agent.
That is the time I pulled the plug. And, I suspect, when the donations get solicited. If you want to take a peek, be warned.
There appear to be many sites that are a front end for the "magnetic recycling generators". I would imagine that the OP has looked over several of them. I remind one and all: the perpetual motion machines all fail to work.