I'd let you do it if paid 1 capacity for it. Otherwise no.
Why the 1 capacity?
The module goes into the deck, not the arm. The deck goes in the arm. Would I have to pay 1 capacity if my deck had the hardening module (or any other module)?
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I forgot about Add a module under Device Modifications. Still per RAW there is no need for any capacity to be used if the cyberarm is modded to have the induction module. Only two packs of parts are needed. The following question would be does the inducting cyberarm allow you use of your direct connection with your deck.
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I'd say yes, as per my original answer. Direct connection between your deck and arm + direct connection between your arm and device = direct connection between deck and device.
I'd allow it, anyway. I dare say RAW supports it too, with every device having a universal connector you ahouldbbe able to connect your deck to your arm, and with the induction receiver mod on your arm you'll have a direct connection to whatever device you touch.
Hmm, gives new meaning to the networking term "handshake"