[cactusbob]

Just get some crimp connectors for the spade terminals. I think you can even get adaptors in Halfrauds for this kind of thing.

 

[cactusbob]

If you get the ones with a soft rubbery insulator that slides off you can just solder them to the wire. Or just remove the insulator altogether, solder it on and then put some heat shrink tubing over the top.

As far as getting them to stick on properly in the first place a proper crimp tool is the best way rather than pliers. Pliers tend to crush the connector whereas a crimp tool will apply the correct pressure all the way around the connector.

 

[cactusbob]

The connectors in the space on your speaker are just spade terminals. If you get the matching connector you can stick it on the speaker wire and then just slide it onto those spade connectors.

Something like these will do the job