Asma Aweys, 30, Abdulaziz Abu Munye, 27, and Ahmed Aweys, 33, were sentenced to 19 months, 15 months and 25 months behind bars.
Mum-of-two Aweys, from Edmonton in north London, said Ariana was "the devil", in the wake of the Manchester bombing in a message recovered by police.
Describing the Westminster attack, she said: "This was by the decree of Allah."
Judge Mark Dennis QC dismissed an argument made by Ms Aweys's defence barrister Rhiannon Crimmins.
He said: "The WhatsApp messaging speaks volumes," before adding, "It is apparent that other adults related to the defendants shared similar views and varying degrees of support for the extremist cause."
Ms Aweys was also found to have three copies of the English language IS magazine Rumiyah on her phone last April.
TERROR HOW TO GUIDES
Articles in the publications offered advice such as how to "inflict misery and destruction on the enemies of Allah" through methods including vehicle attacks.
Tips on the best way to injure people using knives, including which type of blade is most effective, were also contained in the magazines.
There was also information about how to make Molotov cocktails and napalm to be used in arson attacks.
Ms Crimmins, defence counsel for Ms Aweys, said: "I think she has been greatly shocked by her arrest."
This has "caused her to reflect" on her actions, Ms Crimmins said, adding: "In particular she feels she has let down her children."
Last month Ms Aweys pleaded guilty to collecting three copies of the magazine in November and December 2016 and January 2017.
Mr Munye, who lived with Ms Aweys, previously admitted sending a 58-minute IS propaganda video, called Flames Of War 2, to Mr Aweys, of Chadwell Heath in east London.
This was by the decree of Allah
The video contained footage of brutal executions, battle scenes and references to attacks in the West.
Osama bin Laden also appeared in the film, as well as images of rockets heading towards the US.
Afterwards the pair discussed the footage, with one message reading: "Bowling with kafir heads… lol."
Mr Aweys then forwarded the video to a further three people, including his wife.
He said to one recipient: "Tell the world."
The trio came to police attention after Mr Aweys was arrested over a separate matter and had his electronic devices seized.
Ms Aweys was sentenced for two counts of collecting publications useful to a terrorist, Mr Aweys for three counts of disseminating terrorist material and Mr Munye for one count of disseminating terrorist material.
Acting Commander Alexis Boon, head of the Met's counter terrorism command, said: "Counter terrorism and Flying Squad officers worked together to apprehend three brothers involved in a conspiracy to burgle a jeweller's.
"Afterward, when we saw what was on Ahmed Aweys' phone, the investigation quickly escalated into a terrorism probe involving him, his sister and her husband.
"In their Whatsapp conversations, Ahmed Aweys and Abdulaziz Munye laughed about a sickening video that showed people being brutally executed by terrorists.
"It is obvious they fully support the murder of innocent people for terrorist purposes, so I am pleased that my officers have ensured they are no longer free to continue peddling this toxic propaganda.
"Asma Aweys was avidly collecting guides intended to help terrorists kill large groups of people. These guides, if provided to the wrong person, would have given them sufficient advice to be able to carry out an immensely harmful attack.
"Instead, this material is now out of her hands."
Source: Read Full Article