Config. of MX record to use external mailserver

hello,
i am curiose on how to config. the MX record to get mailed all e-mail to my local PC.
I know i can change the MX record and put my static IP to forward the e-mails. However if i turn Off my local pc i lost all e-mails (they do not bounce back to the server but has ben lost - seems a blackhole) Is there any way to let e-mails on the server (in query/cache) and if i turn On my PC they will be delivered?

Thanks

 

 

 

 

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