[MCF]

The proof that Obama ordered it is the fact that he signed the executive order to relax the rules constraining information sharing on the NSA right before leaving office. A person would have to be willfully blind not to see this:
https://www.nytimes.com/2017/01/12/us/politics/nsa-gets-more-latitude-to-share-intercepted-communications.html?_r=0

[plangent]

Something is missing in the Obama push-back. “Approve” could easily be taken to mean “signed”. “Order” could be taken to verbally instruct the action.

What is not said in the Obama denials is the word “initiate”, as in “Loretta, what we need is more information on what this guy is doing. You know, it could affect the national security.”

[Yardstick]

The only caveat is that Obama had been working on a “new framework” that relaxed the intel sharing rules for years, and in fact had announced in early 2016 the coming implementation of the new rules:

https://www.nytimes.com/2016/02/26/us/politics/obama-administration-set-to-expand-sharing-of-data-that-nsa-intercepts.html?action=click&contentCollection=Politics&module=RelatedCoverage&region=EndOfArticle&pgtype=article

In other words, it’s possible Obama would have done this even if the Trump situation hadn’t existed.