Just found out that installing NPM on a system that already has a Solarwinds product installed, or uses the same database that another product is using, is subject to compatibility restrictions. In our case, the latest licensed NPM version is 10.5 and it's incompatible (and unsupported when installed together) with SAM 6.1.1. See "Compatibility of SolarWinds Orion Products for Installation and Upgrade" KB.
More than that (and I hope this saves someone else's bacon): according to support, there's no downgrade path, i.e. you can't downgrade from SAM 6.1.1 to 5.5 and keep your data and stats. In other words, to answer one of the questions in the OP...
"what is the procedure to transfer the NPM license to the newer server - which only has SAM on it?"
... the answer should contain: "check that the combination of products you plan to run on the same box or pointing to the same database is supported". E.g. SAM 6.1.1 and NPM 10.5 are not.
(Related thread: {KeepAlive} (and some other) variables not getting populated.)