Sorry, was doing an item no search in ebay.
Looks like it should do it. Best advice is to ask the seller if it will pass a 4k signal direct to the screen connected out of port HDMI 1. If they say yes, then you can return it if it fails to work.
Make sure you've got the correct cables and make sure all 3 are the same. Try getting a small F-F coupler to test 2 joined together from the box to the screen, before you put the splitter in circuit. Then connect the unit in place of the coupler, and remember to apply power to it. Power everything off (at the wall, not standby), wait a minute, and then power it up again and re-test. Then do a separate test, from the solo 4k direct to the HDMI->composite convertor and make sure that works as expected. Finally connect it all together in its final config and test. Full power down again and then re-test.
Cables can be cause a lot of the problems, with no one make or supplier more reliable than any other, and price is no guarantee either. The biggest issue seems to be CEC, though some cables fail on HDCP. Neither of these protocols should be an issue to you, as I don't think the Solo 4k bothers sending HDCP, and you didn't say you were using CEC. Try a couple of low cost cables first, before you splash out big bucks (I've used plusbee, rhino cables and kenable sellers on ebay).
Hope this helps
