Packets go out one LAN machine but do not reach another one

I have a pretty simple topology.
Machine 1:

ip a
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000
    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
    inet 127.0.0.1/8 scope host lo
       valid_lft forever preferred_lft forever
    inet6 ::1/128 scope host 
       valid_lft forever preferred_lft forever
2: eth0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP group default qlen 1000
    link/ether 00:15:5d:0d:2c:a2 brd ff:ff:ff:ff:ff:ff
    inet 193.124.117.195/24 scope global eth0
       valid_lft forever preferred_lft forever
    inet6 fe80::215:5dff:fe0d:2ca2/64 scope link 
       valid_lft forever preferred_lft forever
3: eth1: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP group default qlen 1000
    link/ether 00:15:5d:0d:2c:a5 brd ff:ff:ff:ff:ff:ff
    inet 192.168.0.2/24 scope global eth1
       valid_lft forever preferred_lft forever
    inet6 fe80::215:5dff:fe0d:2ca5/64 scope link 
       valid_lft forever preferred_lft forever
ip r
default via 193.124.117.1 dev eth0 
192.168.0.0/24 dev eth1 proto kernel scope link src 192.168.0.2 
193.124.117.0/24 dev eth0 proto kernel scope link src 193.124.117.195 

Machine 2:

ip a
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000
    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
    inet 127.0.0.1/8 scope host lo
       valid_lft forever preferred_lft forever
    inet6 ::1/128 scope host 
       valid_lft forever preferred_lft forever
2: eth0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP group default qlen 1000
    link/ether 00:15:5d:0d:2c:a3 brd ff:ff:ff:ff:ff:ff
    inet 176.113.82.77/24 scope global eth0
       valid_lft forever preferred_lft forever
    inet6 fe80::215:5dff:fe0d:2ca3/64 scope link 
       valid_lft forever preferred_lft forever
3: eth1: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP group default qlen 1000
    link/ether 00:15:5d:0d:2c:a4 brd ff:ff:ff:ff:ff:ff
    inet 192.168.0.3/24 scope global eth1
       valid_lft forever preferred_lft forever
    inet6 fe80::215:5dff:fe0d:2ca4/64 scope link 
       valid_lft forever preferred_lft forever
ip r
default via 176.113.82.1 dev eth0 
176.113.82.0/24 dev eth0 proto kernel scope link src 176.113.82.77 
192.168.0.0/24 dev eth1 proto kernel scope link src 192.168.0.3 

Ping 192.168.0.3 -> 192.168.0.2:

ping -c 1 192.168.0.2
PING 192.168.0.2 (192.168.0.2) 56(84) bytes of data.
64 bytes from 192.168.0.2: icmp_seq=1 ttl=64 time=1.63 ms

--- 192.168.0.2 ping statistics ---
1 packets transmitted, 1 received, 0% packet loss, time 0ms
rtt min/avg/max/mdev = 1.629/1.629/1.629/0.000 ms

Ping 192.168.0.2 -> 192.168.0.3:

ping -c 1 192.168.0.3
PING 192.168.0.3 (192.168.0.3) 56(84) bytes of data.
64 bytes from 192.168.0.3: icmp_seq=1 ttl=64 time=2.70 ms

--- 192.168.0.3 ping statistics ---
1 packets transmitted, 1 received, 0% packet loss, time 0ms
rtt min/avg/max/mdev = 2.702/2.702/2.702/0.000 ms

Next. I have Nginx on the 192.168.0.3 machine, but it does not really matter. I want to implement port forwarding from 192.168.0.2:8888 to 192.168.0.3:80. I check connection:

wget 192.168.0.3:80
--2023-06-14 19:02:52--  http://192.168.0.3/
Connecting to 192.168.0.3:80... connected.
HTTP request sent, awaiting response... 200 OK

Then I add a rule on 192.168.0.2 machine

iptables -t nat -A PREROUTING -p tcp --dport 8888 -DNAT --to 192.168.0.3:80

And turn forwarding on:

echo 1 > /proc/sys/net/ipv4/ip_forward

Then I try to open 193.124.117.195:8888 from the third machine and see that packets go out the first one (192.168.0.2):

tcpdump -i eth1
tcpdump: verbose output suppressed, use -v or -vv for full protocol decode
listening on eth1, link-type EN10MB (Ethernet), capture size 262144 bytes
19:18:33.480948 IP 84.252.147.253.6016 > 192.168.0.3.http: Flags [S], seq 2692986583, win 12500, options [mss 1250,nop,wscale 2,sackOK,TS val 3132330242 ecr 0], length 0
19:18:36.480279 IP 84.252.147.253.6016 > 192.168.0.3.http: Flags [S], seq 2692986583, win 12500, options [mss 1250,nop,wscale 2,sackOK,TS val 3132333242 ecr 0], length 0

And also I add another rule to see that packets go in the right direction:

iptables -t nat -A POSTROUTING -p tcp --dport 80 -d 192.168.0.3 -j ACCEPT
iptables -t nat -nvL POSTROUTING 
Chain POSTROUTING (policy ACCEPT 0 packets, 0 bytes)
 pkts bytes target     prot opt in     out     source               destination         
    2   120 ACCEPT     tcp  --  *      *       0.0.0.0/0            192.168.0.3          tcp dpt:80

So, as I unsderstand packets go through the eth1 to local network and should reach Machine 2. But nothing happens here. I try to listen 192.168.0.3 eth1 and see only arp packets. Also iptables shows no packets. Where have I done a mistake ? 192.168.0.3:

tcpdump -i eth1
tcpdump: verbose output suppressed, use -v or -vv for full protocol decode
listening on eth1, link-type EN10MB (Ethernet), capture size 262144 bytes
19:29:13.020569 ARP, Request who-has 192.168.0.3 tell 192.168.0.2, length 28
19:29:13.020600 ARP, Reply 192.168.0.3 is-at 00:15:5d:0d:2c:a4 (oui Unknown), length 28

I found an answer: Just added MASQUERADE to mask source ip of LAN packet:

iptables -t nat -A POSTROUTING -p tcp -d 192.168.0.3 --dport 80 -j MASQUERADE