Dwyer returns to the club he featured for in 2021/22. Before his arrival at Whitebank Stadium, the centre-back had spells at Prestwich Heys and Chadderton.
He went on to make 34 appearances for Wythenshawe Town in the NWCFL last season before following James Kinsey to Stalybridge following the conclusion of the campaign.
However, he has yet to feature for the club so far in 2023/24.
Avro have also confirmed that Celtic have waived their seven-day notice of approach for the player, meaning he is eligible to feature against City of Liverpool on Wednesday night.
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