You had been asked to do 100%, you provide 120%. 100% is your work and you include an additional 20% that you admittedly got from somewhere else to improve the 100%. That is good, as long as you explain it in your documentation : Don't try to fool your client.
Best Case scenario : either you negotiate some delay with your client (late fee penalilities), or you explain to him that you will buy some work from another company and you'll provide it to your client instead of your work. That is fine, but you earn no money at all for yourself for the work you haven't done. Just for the integration and the providing of a solution !....few marks !
Next step, You don't tell it to your client and he discovers it by itself. He decides that he could not trust you anymore. You lose all the contract with that client ... and perhaps from other client who will hear that story !
Worst Case : the client pay twice for the same product (once from you and once from the other company that allows you to reuse their product). He doesn't care about which provider made the mistake. He just get rid of the two of them.
What about doubt ...
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