Can is used to talk about permission that has already been given or refused, and about things that are allowed by rules or laws. May is not notmally used in this way.
(from Practical English Usage 4th ed. by Michael Swan)
Can "Do we have his general permission (which has already been given) to smoke in his garden?" be paraphrased to "May we smoke in his garden?"? (Here, "general permission" means the permission to do something at any time .)
From P.E.U, I know "Do we have his general permission (which has already been given) to smoke in his garden?" can be paraphrased to "Can we smoke in his garden?".
Can "Do we have your general permission (which has already been given) to smoke in your garden?" be paraphrased to "May we smoke in your garden?"? (Here, "general permission" means the permission to do something at any time .)
From P.E.U, I know "Do we have your general permission (which has already been given) to smoke in your garden?" can be paraphrased to "Can we smoke in your garden?".