Looks like this may not be happening. 

June 2022
Shetland Times reports plans to convert to a mosque
https://www.shetlandtimes.co.uk/2022/06/20/plans-lodged-to-convert-former-shop-into-place-of-worship-for-muslim-community

Oct 2024
Ratings list for Scotland gives ratable value of £5,800
effective from 01-APR-23. Occupier/proprietor is not the person referred to as the promoter of the mosque:
https://www.saa.gov.uk/search/?SEARCHED=1&SEARCH_TABLE=valuation_roll_cpsplit&SEARCH_TERM=ZE1+0PJ%2C+LERWICK&searchtype=listing&DISPLAY_COUNT=10&ASSESSOR_ID=&TYPE_FLAG=C&ORDER_BY=PROPERTY_ADDRESS&H_ORDER_BY=SET+DESC&R_ORDER_BY=SET+DESC&DRILL_SEARCH_TERM=LERWICK&DD_TOWN=LERWICK&DISPLAY_MODE=FULL&type_flag=C&UARN=11%2F20%2F586090%2F0&PPRN=2439&ASSESSOR_IDX=11#results