In 2010 Rimkus moved to Lithuania, signing a one-year contract with FK Ekranas. He became the highest scorer of the team that season with 15 goals in 26 matches respectively, just one goal behind the top scorer of the league Povilas Lukšys. After the season Rimkus moved to Cyprus, signing a half-season contract with the Cypriot Fourth Division club Finikas Ayias Marinas Chrysochous. In July 2011 he returned to Latvia and signed a contract with the Latvian Higher League newcomers FC Jūrmala. Despite joining in mid-season, with 10 goals in 18 games he became the team's highest scorer in the league. In March 2012 Rimkus was signed by the Latvian Higher League newcomers FK Spartaks Jūrmala, but after just playing 1 match he was released.