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Liz quoted Cruz as claiming: "I didn't know I was supposed to tell the FEC I borrowed over a million from my Wall Street margin accounts to fund my campaign."

Trading on margin is something that was never attractive to me since I valued my principal too greatly.

However, my understanding of buying stocks on margin from a broker is that the broker maintains possession of the purchased shares.

For example, if I purchase $100,000 worth of stock on margin I might be expected to put up $20,000 and the broker will lend $80,000 toward that purchase, retaining the shares themselves.

The broker then monitors the account to ensure that the shares retain sufficient value to pay off the loan. If, for example, the share prices dropped to the point that it would take 90% of the share values to pay off the loan, then the investor receives a "margin call". That is, the broker contacts the investor and expects the investor to put up more cash so that the margin is re-established.

If the investor is unable to meet the requirements of the margin call, then the broker sells the stock, pays off the loan, and returns any residual to the investor.

So, my question regarding Cruz is: How could Cruz make use of stock shares that by law must be retained by the broker?

The charge against Cruz doesn't make sense to me. What is it that Cruz did wrong in this instance? Did the broker violate the law?

...the broker will lend $80,000 toward that purchase, retaining the shares themselves.

You provided the operative words. If the shares become worth less than $80,000 before the broker can prudently liquidate, the broker then has a legally enforceable claim for the diminished value. In this setting, the prospective presidential candidate would be obligated to the claim holder.