A dependent must be citizen or resident of U.S. If your mother, completes substantial presence test in the year, she is resident for tax purposes. You may be able to claim her if you meet the other requirements:
You provided more than half of her support and she did not earn more than $3,650 (worldwide income) in the year.

QUOTE," If your mother, completes substantial presence test in the year, she is resident for tax purposes. . . " Agreed! Yes, that is possible as your mother will be considered a US resident alient.if your mother,a visitor, stays in US for 183 days anyhow, then , she is considered as a resident alien UNDER the US Tax code, not under the US INS Rule. So in that case you can claim her as your dependent.

Note that the B-1 visa normally is good for only six months. This is BY DESIGN to prevent the visa holder from meeting the Substantial Presence Test and be eligible to be claimed as dependents.

QUOTE," Note that the B-1 visa normally is good for only six months."---Yes. Absolutely TRUE; in general, his mother can not change her visa staus if she enters into USA on a B1/B2 visa. However,she may change her visa status to a non-immigrant visa sttus depends if she qualifies and finds a employer who can sponsor and process a working visa for her.

If his mother entered into USA on a Visa Waiver basis(With the visa waiver, there is no way the depenent can change to any other visa status (except for "spouse of US citizen"), then shewould have to leave the USA before her 90 days are up).