Windows 7 PC can't find wireless printer...

HP windows 7 PC can't find HP wireless printer connected to network (wirelessly); but if that printer is hardwired to router, the PC can find it wirelessly. The printer is able to connect to internet to update apps, etc.; and HP ePrint address works with the printer.
IF I connect the printer to the routers with cat 5 cable, then the PC can find the printer and print to it without issue.
It is important to me because soon due to a move, the printer will NOT be near the router to be able to hardwire.
Thank you for reasonable solutions!

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Clarification Request
This sounds like the printer is not paired to the router.

I don't see which HP but all of them told us how to pair with our WiFi router.

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thanks for reply, but...

Thanks for the reply, sorry things were not clearer. Via wireless connection, the Router DOES find the printer and the printer DOES show connected and the printer IS able to get to the internet/HP site to update apps, receive prints via ePrint, etc. However the PC cannot find the printer when connected to router via wireless.

Things work fine only if the printer is directly cabled into the router; then the PC instantly locates the printer and all is good.

I'm trying to figure out why the PC can't find the printer when printer connected to the router wirelessly because in the near future the printer will not be close enough to the router to hardwire the connection.

thanks again for taking the time to reply.

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This sounds like the old firewall in the router issue.
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will research thanks

Traveling right now but will check out that possibility when I return. The router is AT&T Arris so I have to research for settings on that unit.

thanks for the reply and the links to the past explanations.

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