I get Leishmania infantum from infected mice just removing aseptically the spleen from these animals and placing the entire organ or fragments in culture flasks with RPMI + fetal calf serum. Within 15 days the promastigotes will begin to be released. it is possible to use a cell strainer, but is not necessary.
If you want to obtain intracellular amastigotes, you have to macerate the spleen and isolate the parasite. There is an interesting methodology in this paper "Regulation of the expression of nitric oxide synthase and leishmanicidal activity by glycoconjugates of Leishmania lipophosphoglycan in murine macrophages". We use this methodology to isolate amastigotes from lineage (J774A1) infected macrophages.
I assume you meant in vitro culturing promastigotes, which is readily achievable for many Leishmania spp. In general you will have promastigotes in culture in a couple of days up to a week. You collect the spleen from infected mice, mince it and wash with PBS, and transfer to culture medium, which should have a neutral pH. Of course all procedures should be performed under sterile conditions to avoid bacterial contamination.
Remove the spleen aseptically and homogenized in Locke’s solution. Centrifuged at 1000 rpm for 5-7 min at 4°C to remove tissue debris. Centrifuge the supernatant at 3000 rpm for 8-10 min, wash the pellet twice with sterile PBS . Culture the isolated parasite in appropriated medium with neutral pH.