It's been just over a month since Alex Pretti was shot and killed during a chaotic immigration enforcement operation in Minneapolis ... and on what would have been his 38th birthday, his mom is pouring her heart out online.

Pretti's mom shared a touching Instagram tribute Sunday, posting a smiling photo of her son standing in front of a rocky desert landscape. Over the image, she wrote about the pain of losing him, saying when you lose a child, you lose more than just a child ... you lose a piece of your heart and part of your future.

She added his laughter, smile and love will remain with her forever, calling him her "precious boy" who will never fade from her soul.

As we reported ... Pretti, a Minneapolis ICU nurse, was shot and killed in January during an immigration enforcement operation while federal agents were conducting what officials described as a targeted action when gunfire erupted.

In February, the Hennepin County Medical Examiner officially ruled Pretti's death a homicide, confirming he died from multiple gunshot wounds. Authorities have said the shooting occurred during a tense confrontation, while Pretti's family and supporters insist he did not brandish a weapon nor pose as a threat.

His death sparked protests and calls for transparency as federal investigators began reviewing the incident.