The 1975's Matty Healy Shares Message for Girlfriend FKA twigs After Shia LaBeouf Abuse Allegations

Matty Healy is sticking by his girlfriend FKA twigs after she filed a lawsuit against her ex-boyfriend Shia LaBeouf alleging "relentless" abuse last week.

Posting a candid photo of the "cellophane" songstress on his Instagram Sunday, The 1975 frontman, 31, wrote a sweet caption dedicated to Twigs, calling her a "legend," "icon" and "loml" or "love of my life" in an emoji-filled caption.

"Bro an sis vibes awe cuties xxx," commented Louis Healy, Matty's brother.

"So proud ❤️❤️❤️❤️❤️," added actress Denise Welch, Matty's mother.

On Monday, Twigs, 32, was also spotted taking a stroll in North London wearing a long warm coat and glasses and taking a phone call.

The post from Healy comes days after Twigs filed a lawsuit on Dec. 11 alleging that LaBeouf sexually and physically assaulted her during their relationship, according to documents obtained by PEOPLE.

"What I went through with Shia was the worst thing I've ever been through in the whole of my life," she told the New York Times, going on to say that she didn't go to the police at first to not harm his career and because she "thought her account would not be taken seriously."

Over the weekend, singer Sia also came out with allegations against the Honey Boy actor, whom she said "conned" her into "an adulterous relationship claiming to be single."

Twigs offered her support to the "Chandelier" singer, 44, adding that her claim "reinforces why i had to publicly share my experience."

RELATED VIDEO: FKA Twigs Sues Ex-Boyfriend Shia LaBeouf for 'Relentless' Sexual, Physical and Emotional Abuse

"we need to support each other <3," she tweeted, before adding, "you're an inspiration and thank you everyone for your love and solidarity."

While a rep for LaBeouf has not commented to PEOPLE, he did address the allegations from Twigs in several emails to the New York Times saying that he was in no position "to tell anyone how my behavior made them feel."

"I have no excuses for my alcoholism or aggression, only rationalizations. I have been abusive to myself and everyone around me for years," he wrote to the newspaper. "I have a history of hurting the people closest to me. I'm ashamed of that history and am sorry to those I hurt. There is nothing else I can really say."

As for Twigs and Healy — the musical couple has been together since early February when Healy shared a photo of the two on Instagram following the NME Awards. (A source confirmed the relationship news to PEOPLE.)

If you are experiencing domestic violence, call the National Domestic Violence Hotline at 1-800-799-7233, or go to thehotline.org. All calls are toll-free and confidential. The hotline is available 24/7 in more than 170 languages.