So you probably already read that so far as adding the business to Google local is concerned, PO boxes are violation of Google local quality guidelines - if you read through them, they are looking for places that receive customers and they specifically state that post office boxes aren't considered physical locations. So if you add them as a listing to Google local, they get deleted, sometimes .. pretty often (there are still some listings with PO boxes but I wouldn't bother trying). And you want your website address/phone etc to match your local listing for good local SEO. So although you could add the various PO boxes to the website, I don't think it will help for local, there's probably no real point them being on there unless they have some legitimate business use and I wouldn't recommend it.
I've mused recently (in a blog post) that using virtual offices combined with local area code numbers (e.g. forwarded to the main sales number) might work for boosting local, but only if the business centre allows use of the address rather than the PO box address. If you had the virtual office address but didn't have local matching numbers, I think that'd be a potential negative for local. I think there's an element of risk here as virtual offices aren't too difficult to spot and let's face it, it is still against the quality guidelines and trying to manipulate results etc. I'd kind of be interested to know if it'd work but I wouldn't try it for a client myself!
Things the client can do instead -
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Use his one business address, phone etc, same on local listing as on website, and then,
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Specify in his Google local listing which areas he covers. Rather than stating the whole of the UK, I'd recommend adding those specific areas he wants to rank for.
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Create pages for those areas around what people search for e.g. going for the organic results 'electrician services in lincoln' etc as Google does still feature these around the local listings.
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Add location specific content for that area - eg. case studies, testimonials for companies / customers in that area with plenty of refs to the location.
Hope that helps.