I'm not an expert on this topic but I believe she can go to the border and seek admittance. she'll be there awhile until they can verify who she is. She explain to CBP what happened.

File online to get the card replaced as lost. but the fee is a little high. Gorm I90 and it cost about $500

Coincido con @William u, tampoco soy experta pero mi esposo fue víctimas de robo en la frontera de México (su cartera con tarjeta verde) el se dirigió al ministerio público a reportar el robo y le dieron un reporte de policía indicando lo que le habían robado) se se dirigió al puerto de entrada para regresar a Estados Unidos y le explicó al agente lo que sucedió y le mostró el reporte de policía. Lo tuvieron un momento para verificar su identidad y le dieron un permiso de entrada por única vez y le indicaron que al regresar a casa iniciará su trámite con el formulario I-90 (solicitud para reemplazar la tarjeta verde) indicando en dicho formulario la opción “que su tarjeta verde estaba extraviada”. Hizo dicho trámite y mientras esperaba que se procesara su formulario I-90, solicitó un sello ADIT para poder seguir viajando a México y regresar sin problema. Al cruzar la frontera el mostraba el sello ADIT, el recibo de pago para el reemplazado de su tarjeta verde y la carta que indicaba que sus datos biométricos ya habían sido tomados. Sello ADIT (Documentación de Extranjero, Identificación y Telecomunicaciones) es un documento muy importante que inmigración utiliza para proporcionar una prueba temporal del estatus de residente permanente legal y se coloca en una página del pasaporte de un inmigrante o directamente en su tarjeta de residencia. Mi esposo no tenía vigente su pasaporte y obviamente tampoco su tarjeta verde por lo que solo le pidieron llevar 2 fotografías tamaño pasaporte e identificación y pegaron una fotografía en un cartoncillo pequeño (formulario I-94) con sus datos y se lo sellaron vigente por un año. Si el sello ADIT se vence mientras el reemplazo de la tarjeta verde aún no concluye puede volver a renovarlo.

I agree with you @William u, I am not an expert either but my husband was a victim of robbery on the border of Mexico (his wallet with a green card) he went to the public ministry to report the theft and they gave him a police report indicating what had been stolen from him) He went to the port of entry to return to the United States and explained to the agent what happened and showed him the police report. They took him a moment to verify his identity and gave him a one-time entry permit and told him that when he returned home he would begin his process with the I-90 form (application to replace the green card) indicating on said form the option “ that his green card was lost.” He completed this procedure and while waiting for his I-90 form to be processed, he requested an ADIT stamp so he could continue traveling to Mexico and return without problem. Upon crossing the border he showed the ADIT stamp, the payment receipt for the replacement of his green card and the letter indicating that his biometric data had already been taken. ADIT Stamp (Alien Documentation, Identification and Telecommunications) is a very important document that immigration uses to provide temporary proof of legal permanent resident status and is placed on a page of an immigrant's passport or directly on their residence card. My husband did not have a valid passport and obviously neither did his green card, so they only asked him to bring 2 passport-sized photographs and identification and they pasted a photograph on a small piece of cardboard (form I-94) with his information and stamped it valid for one year. If the ADIT seal expires while the green card replacement has not yet been completed, you can renew it.

if he stole her property sounds like she needs to call the cops and then get a restraining order put on this guy.

@singer nogerbo Thank you for letting us know, good to know the details.

@William @w s @singer nogerbo @Perla N thanks for the info I would let her know Thank you everyone